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Answers posted by thanvigandhi_1
Questions
3013
answers
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best answers
0
votes
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse : $ \large\frac{x^2}{36}$$+\large\frac{y^2}{16}$$=1$
answered
Jul 15, 2014
Toolbox:Equation of an ellipse along major axis is $\large\frac{x^2}{a^2}$$+\large\frac{y^2}{b^2}$$=...
0
votes
Find the equation of the parabola that satisfies the given conditions : Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis
answered
Jul 15, 2014
Toolbox:Equation of the parabola along y - axis and opening upwards is $x^2=4ay$Equation of the para...
0
votes
Find the equation of the parabola that satisfies the given conditions : Vertex (0,0) passing through (2,3) and axis is along x-axis
answered
Jul 15, 2014
Toolbox:Equation of a parabola along the x - axis and opening rightward is $ y^2=4ax$Equation of a p...
0
votes
Find the equation of the parabola that satisfies the given conditions : Vertex (0,0); focus (–2,0)
answered
Jul 14, 2014
Toolbox:If the coordinates of the focus is (-a, 0)The equation of the parabola is $y^2=-4ax $ and th...
0
votes
Find the equation of the parabola that satisfies the given conditions : Vertex (0,0); focus (3,0)
answered
Jul 14, 2014
Toolbox:If the coordinates of focis is (a, 0) then the parabola is open rightward.The equaton of the...
0
votes
Find the equation of the parabola that satisfies the given conditions : Focus (0,–3); directrix y = 3
answered
Jul 14, 2014
Toolbox:If the coordinates of the focus is (0, -a) then the parabola is open downwards. The equation...
0
votes
Find the equation of the parabola that satisfies the given conditions : Focus (6,0); directrix x = – 6
answered
Jul 14, 2014
Toolbox:If the coordinates of focis is (a, 0) then the parabola is open rightward.The equaton of the...
0
votes
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ x^2=-9y$
answered
Jul 14, 2014
Toolbox:Equation of the parabola $x^2=-4ay$Since the coefficient of y is negative the curve is open ...
0
votes
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ y^2=10x$
answered
Jul 14, 2014
Toolbox:Equation of a parabola is $y^2=4ax$If x is positive , then the parabola opens towards the ri...
0
votes
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ x^2=-16y$
answered
Jul 14, 2014
Toolbox:Equation of the parabola $x^2=-4ay$Since the coefficient of y is negative the curve is open ...
0
votes
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ y^2=-8x$
answered
Jul 14, 2014
Toolbox:Equation of the parabola is $y^2=-4ax$Since the coefficient of x is negative. Hence the para...
0
votes
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ x^2=6y$
answered
Jul 14, 2014
Toolbox:Equation of the parabola $x^2=4ay$If the coefficient of y is positive, the parabola opens up...
0
votes
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum for the following : $ y^2=12x$
answered
Jul 14, 2014
Toolbox:Equation of a parabola is $y^2=4ax$If x is positive , then the parabola opens towards the ri...
0
votes
Does the point (–2.5, 3.5) lie inside, outside or on the circle $x^2 + y^2 = 25$ ?
answered
Jul 14, 2014
Toolbox:If the distance between the point through which the circle passes say $(x_1, y_1)$ is less t...
0
votes
Find the equation of a circle with centre $(2,2)$ and passes through the point $(4,5)$.
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Distan...
0
votes
Find the equation of the circle passing through $(0,0)$ and making intercepts a and b on the coordinate axes.
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Step 1...
0
votes
Find the equation of the circle with radius $5$ whose centre lies on x-axis and passes through the point $(2,3)$.
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Step 1...
0
votes
Find the equation of the circle passing through the points $(2,3)$ and $(–1,1)$ and whose centre is on the line $x–3y–11 = 0$.
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Step 1...
0
votes
Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Step 1...
0
votes
$2x^2 + 2y^2 – x = 0$, find the centre and the radius of the circles.
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$The eq...
0
votes
$x^2+y^2–8x+10y–12=0$, find the centre and radius of the circles.
answered
Jul 13, 2014
Toolbox:Equation of a circle with centre (h,k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Equati...
0
votes
$x^2+ y^2– 4x–8y–45=0$ find the centre and radius of the circles.
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$Equa...
0
votes
$(x+5)^2+(y-3)^2=36$ find the centre and radius of the circles.
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$The ...
0
votes
Find the equation of the circle with centre (–a, –b) and radius $ \sqrt{a^2-b^2}$
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$The ...
0
votes
Find the equation of the circle with centre (1,1) and radius $ \sqrt 2$
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$The ...
0
votes
Find the equation of the circle with centre $ \bigg( \large\frac{1}{2}$$, \large\frac{1}{4} \bigg)$ and radius $ \large\frac{1}{12}$
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$The ...
0
votes
Find the equation of the circle with centre (–2,3) and radius 4
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as : $(x-h)^2+(y-k)^2=r^2$The ...
0
votes
Find the equation of the circle with centre (0,2) and radius 2
answered
Jul 11, 2014
Toolbox:Equation of a circle with centre (h, k) and radius r is given as $ (x-h)^2+(y-k)^2=r^2$Given...
0
votes
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle.
answered
Jul 11, 2014
Toolbox:Equation of a line parallel to x axis is y = constant.Equation of a line parallel to y axis ...
0
votes
Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following : The equation of the line through the intersection of the lines 2x – 3y = 0 and4x – 5y = 2 and
answered
Jul 11, 2014
Toolbox:Equation of a line passing through the intersection of two lines $a_1x+b_1y+c_1=0$ and $ a_2...
0
votes
Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following : The value of the $ \lambda$, if the lines $(2x + 3y + 4) +\lambda (6x – y + 12) = 0 $ are
answered
Jul 9, 2014
Toolbox:Equation of a line parallel to y - axis is x = a constantSlope of a line is $ -\large\frac{...
0
votes
Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following :
answered
Jul 9, 2014
Toolbox:Section formula : $\large\frac{mx_2+mx_1}{m+n}$$, \large\frac{my_2+ny_1}{m+n}$Mid point form...
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votes
State whether the following is true or false and justify : Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
answered
Jul 9, 2014
Toolbox:Slope of a line joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is $ \bigg( \large\frac{y_2...
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votes
State whether the following statement is true or false and justify : The lines $ ax + 2y + 1 = 0, bx + 3y + 1 = 0 $ and $cx + 4y + 1 = 0$ are concurrent if a, b, c are in G.P
answered
Jul 9, 2014
Toolbox:If three lines $ a_1x+b_1y+c_1=0 ; a_2x+b_2y+c_2 = 0 ; a_3x+b_3y+c_3 = 0$ are coplanar then ...
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votes
State whether the following statement is true or false and justify : The equation of the line joining the point (3, 5) to the point of intersection of the lines $4x + y – 1 = 0 $ and $7x – 3y – 35 = 0$ is equidistant from the points (0, 0) and (8, 34)
answered
Jul 9, 2014
Toolbox:Equation of line joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is $ \large\frac{y-y_1}{y_...
0
votes
State whether the following statement is true or false and justify : The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is $x + y = 2$. Then the other two sides are $y - 3 = (2 \pm \sqrt3 ) (x - 2)$.
answered
Jul 9, 2014
Toolbox:Slope of a line $m$ which make an angle $ ' \theta '$ in the positive direction of x axis is...
0
votes
State whether the following statement is true or false and justify : The straight line $5x + 4y = 0$ passes through the point of intersection of the straight lines $x + 2y – 10 = 0$ and $ 2x + y + 5 = 0$
answered
Jul 8, 2014
Toolbox:If three lines are concurrent then $ \begin{vmatrix} a_1 & b_1 & c_1 ...
0
votes
State whether the following statement is true or false and justify : Equation of the line passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \sec \theta + y \: cosec \theta = a $ is $ x \cos \theta - y \sin \theta = a \sin 2 \theta $
answered
Jul 8, 2014
Toolbox:Equation of a line passing through a point $(x_1, y_1)$ and having slope $m$ is $y-y_1=m(x-x...
0
votes
State whether the following statement is true or false and justify : The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear
answered
Jul 8, 2014
Toolbox:Area of a triangle is given by $ \Delta = \large\frac{1}{2} | x_1 (y_2-y_3)+x_2(y_3-y_1)+x_3...
0
votes
Fill in the blank for the following : A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line $ 5x – 12y = 3$ . The equation of its locus is ____.
answered
Jul 8, 2014
Toolbox:Distance between a line $ax+by+c$ from the point $(x_1, y_1)$ is $ d = \bigg| \large\frac{a...
0
votes
Fil in the blank for the following : The points (3, 4) and (2, – 6) are situated on the ____ of the line $3x – 4y – 8 = 0$ .
answered
Jul 8, 2014
Toolbox:The position of the points can be obtained by plotting the points on the graph.https://clay6...
0
votes
Fill in the blank for the the following : Equations of the lines through the point $(3, 2)$ and making an angle of $ 45^{\circ}$ with the line $x-2y=3 $ are _______.
answered
Jul 8, 2014
Toolbox:Slope of an angle is $m = \tan \theta $Angle between two straight lines whose slopes are $m_...
0
votes
Fill in the bank for the following : the line which cuts off equal intercept from the axes and pass through the point (1, -2) is _________.
answered
Jul 8, 2014
Toolbox:Equation of a line in its intercept form is $\large\frac{x}{a}$$ + \large\frac{y}{b}$$=1$ wh...
0
votes
Fill in the blank for the following : If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ____.
answered
Jul 6, 2014
Toolbox:If a,b and c are in A.P then $ \large\frac{a+c}{2}$$=b \quad \Rightarrow a-2b=-c \quad $ (i....
0
votes
Choose the correct answer from the given four options. One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is \[\] [Hint: Let ABC be the equilateral triangle with vertex A (h, k) and let D ($ \alpha , \beta $ ) be the point on BC. Then $ \large\frac{2\alpha + h}{3}$$=0 = \large\frac{2\beta + k}{3}$. Also $ \alpha + \beta -2 = 0$ and $ \bigg( \large\frac{k-0}{h-0} \bigg) $$ \times (-1) =-1]$
answered
Jul 6, 2014
Toolbox:If two lines are perpendicular then the product of their slopes is $m_1m_2=-1$The centroid o...
0
votes
Choose the correct answer from the given four options. The ratio in which the line $3x + 4y + 2 = 0$ divides the distance between the lines $3x + 4y + 5 = 0$ and $3x + 4y – 5 = 0$ is
answered
Jul 6, 2014
Toolbox:The distance between parallel line is $ d = \bigg| \large\frac{c_1-c_2}{\sqrt{a^2+b^2}} \big...
0
votes
Choose the correct answer from the given four options. A line passes through (2, 2) and is perpendicular to the line $3x + y=3$. Its y - intercept is
answered
Jul 6, 2014
Toolbox:Slope of a line which is perpendicular to a line having slope 'm' is $ - \large\frac{1}{m}$....
0
votes
Choose the correct answer from the given four options. A point equidistant from the lines $4x + 3y + 10 = 0, 5x – 12y + 26 = 0$ and $7x+24y-50=0$ is
answered
Jul 6, 2014
Toolbox:Distance of a line $ax+by+c=0$ from a point $(x_1,y_1)$ is $ d = \bigg| \large\frac{ax_1+by_...
0
votes
Choose the correct answer from the given four options. The point (4, 1) undergoes the following two successive transformations : \[\] (i) Reflection about the line $y=x$ \[\] (ii) Translation through a distance 2 units along the positive x-axis \[\] Then the final coordinates of the point are
answered
Jul 6, 2014
Toolbox:When a line undergoes reflection along the line $y=x$, then the coordinates also change as $...
0
votes
Choose the correct answer from the given four options. For specifying a straight line, how many geometrical parameters should be known ?
answered
Jul 6, 2014
Toolbox:To specify a straight line we need at least 2 geometrical parameters.Step 1 :We need to know...
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