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Recent questions tagged conic-sections
Questions
Show that the point $(x,y)$ given by $x=\large\frac{2at}{1+t^2}$ and $y=\large\frac{a(1-t^2)}{1+t^2}$ lies on a circle for all real values of $t$ such that $-1\leq t \leq 1$ where $a$ is any given real numbers.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q2
asked
Oct 17, 2014
by
sreemathi.v
1
answer
Equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$ is
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q59
asked
Oct 17, 2014
by
sreemathi.v
1
answer
The distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$.Its equation is
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q58
asked
Oct 17, 2014
by
sreemathi.v
1
answer
The eccentricity of the hyperbola whose latus rectum is $8$ and conjugate axis is equal to half of the distance between the foci is
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q57
asked
Oct 17, 2014
by
sreemathi.v
1
answer
If $e$ is the eccentricity of the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}\normalsize =1\;(a < b)$,then
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q56
asked
Oct 17, 2014
by
sreemathi.v
1
answer
The length of the latus rectum of the ellipse $3x^2+y^2=12$ is
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q55
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the ellipse whose focus is $(1,-1)$,the directrix the line $x-y-3=0$ and eccentricity $\large\frac{1}{2}$ is
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q54
asked
Oct 16, 2014
by
sreemathi.v
2
answers
If the vertex of the parabola is the point $(-3,0)$ and the directrix is the line $x+5=0$,then its equation is
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
easy
q53
asked
Oct 16, 2014
by
sreemathi.v
1
answer
If the parabola $y^2=4ax$ passes through the point $(3,2)$,then the length of its latus rectum is
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
easy
q52
asked
Oct 16, 2014
by
sreemathi.v
1
answer
If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
easy
q51
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length $3a$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q50
asked
Oct 16, 2014
by
sreemathi.v
1
answer
Equation of the circle with centre on the $y$-axis and passing through the origin and the point $(2,3)$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q49
asked
Oct 16, 2014
by
sreemathi.v
1
answer
Equation of a circle which passes through $(3,6)$ and touches the axes is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q48
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q47
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the hyperbola with vertices at $(0,\pm 6)$ and eccentricity $\large\frac{5}{3}$ is _________ and its foci are ___________
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q46
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the parabola having focus at $(-1,-2)$ and the directrix $x-2y+3=0$ is _________
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q45
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the ellipse having foci $(0,1),(0,-1)$ and minor axis of length $\sqrt 5$ is ____________
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q44
asked
Oct 16, 2014
by
sreemathi.v
1
answer
An ellipse is described by using an endless string which is passed over two pins.If the axes are 6 cm and 4 cm,the length of the string and distance between the pins are ____________
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q43
asked
Oct 16, 2014
by
sreemathi.v
1
answer
The equation of the circle circumscribing the triangle whose sides are the lines $y=x+2,3y=4x,2y=3x$ is _____________
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q42
asked
Oct 15, 2014
by
sreemathi.v
1
answer
The equation of the circle having centre at $(3,-4)$ and touching the line $5x+12y-12=0$ is __________
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q41
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The locus of the point of intersection of lines $\sqrt 3x-y-4\sqrt 3k=0$ and $\sqrt 3kx+ky-4\sqrt 3=0$ for different value of $k$ is a hyperbola whose eccentricity is 2.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q40
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The line $2x+3y=12$ touches the ellipse $\large\frac{x^2}{9}+\frac{y^2}{4}$$=2$ at the point $(3,2)$
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
medium
q39
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : If $P$ is a point the ellipse $\large\frac{x^2}{16}+\frac{y^2}{25}$$=1$ whose foci are $S$ and $S'$,then $PS+PS'=8$.
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q38
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The line $lx+my+n=0$ will touch the parabola $y^2=4ax$ if $ln=am^2$
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q37
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False : The point $(1,2)$ lies inside the circle $x^2+y^2-2x+6y+1=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q36
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False: If the line $lx+my=1$ is a tangent to the circle $x^2+y^2=a^2$,then the point $(l,m)$ lies on a circle.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q35
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False:The shortest distance from the point $(2,-7)$ to the circle $x^2+y^2-14x-10y-151=0$ is equal to $5$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
medium
q34
asked
Oct 15, 2014
by
sreemathi.v
1
answer
State whether the following statement is True or False: The line $x+3y=0$ is a diameter of the circle $x^2+y^2+6x+2y=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-a
easy
q33
asked
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with foci $(0,\pm\sqrt{10})$,passing through $(2,3)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q32-c
asked
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with vertices $(0,\pm 7),e=\large\frac{4}{3}$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
easy
q32-b
asked
Oct 15, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with vertices $(\pm 5,0)$,foci $(\pm 7,0)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
easy
q32-a
asked
Oct 15, 2014
by
sreemathi.v
1
answer
Show that the set of all points such that the difference of their distances from $(4, 0)$ and $(-4, 0)$ is always equal to $2$ represent a hyperbola.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q31
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of the set of all points whose distance from $(0, 4)$ are $\large\frac{2}{3}$ of their distance from the line $y = 9$.
cbse
class11
math
conic-sections
exemplar
sec-b
easy
q30
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of the set of all points the sum of whose distances from the points $(3, 0)$ and $(9, 0)$ is 12.
cbse
class11
math
conic-sections
exemplar
sec-b
medium
q29
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of the following parabola : Focus at $(-1,-2)$,directrix $x-2y+3=0$.
cbse
class11
math
conic-sections
parabola
exemplar
sec-b
easy
q28-c
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of the following parabola : Vertex at $(0,4)$,focus at $(0,2)$.
cbse
class11
math
conic-sections
parabola
exemplar
sec-b
easy
q28-b
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of the following parabola : Directrix $x=0$,focus at $(6,0)$.
cbse
class11
math
conic-sections
parabola
exemplar
sec-b
easy
q28-a
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of a circle passing through the point $(7,3)$ having radius $3$ units and whose centre lies on the line $y=x-1$.
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q27
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of a circle of radius 5 which is touching another circle $x^2+y^2-2x-4y-20=0$ at $(5,5)$.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q26
asked
Oct 14, 2014
by
sreemathi.v
1
answer
Find the equation of a circle whose centre $(3,-1)$ and which cuts off a chord of length $6$ units on the line $2x-5y+18=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-b
medium
q25
asked
Oct 13, 2014
by
sreemathi.v
1
answer
Find the equation of the circle which passes through the points $(2,3)$ and $(4,5)$ and the centre lies on the straight line $y-4x+3=0$.
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q24
asked
Oct 13, 2014
by
sreemathi.v
1
answer
If the lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area 154 square units,then obtain the equation of the circle.
cbse
class11
math
conic-sections
circle
exemplar
sec-c
medium
q23
asked
Oct 13, 2014
by
sreemathi.v
1
answer
Find the equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
medium
q22
asked
Oct 10, 2014
by
sreemathi.v
1
answer
Find the eccentricity of the hyperbola $9y^2-4x^2=36$.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-a
easy
q21
asked
Oct 10, 2014
by
sreemathi.v
1
answer
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$,then obtain equation of the hyperbola.
cbse
class11
math
conic-sections
hyperbola
exemplar
sec-b
medium
q20
asked
Oct 10, 2014
by
sreemathi.v
1
answer
If the line $y=mx+1$ is tangent to the parabola $y^2=4x$ then find the value of $m$.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q19
asked
Oct 10, 2014
by
sreemathi.v
1
answer
If the points $(0,4)$ and $(0,2)$ are respectively the vertex and focus of a parabola,then find the equation of the parabola.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q18
asked
Oct 10, 2014
by
sreemathi.v
1
answer
Find the length of the line-segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola where the line-segment makes an angle $\theta$ to the $x$-axis.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
difficult
q17
asked
Oct 10, 2014
by
sreemathi.v
1
answer
Find the coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is 4.
cbse
class11
math
conic-sections
parabola
exemplar
sec-a
medium
q16
asked
Oct 10, 2014
by
sreemathi.v
1
answer
Find the distance between the directrices of the ellipse $\large\frac{x^2}{36}+\frac{y^2}{20}$$=1$.
cbse
class11
math
conic-sections
ellipse
exemplar
sec-a
easy
q15
asked
Oct 9, 2014
by
sreemathi.v
1
answer
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