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Recent questions in Conic Sections

Questions >> CBSE XI >> Math >> Conic Sections

Let $(x_1,y_1)$ be the point of intersection of the tangent to the parabola $y^2=4ax$ at the points $t_1$ and $t_2$ . Then $x_1=a{t_1}{t_2}$ and $y_1=a(t_1+t_2)$

asked Feb 20, 2015 by tanvirahmedodesk

1 answer

how to remember equation of tangent . can you show how did you find out Equation of tangent at $(a{t_1}^2,2a{t_1})$ is

asked Feb 19, 2015 by tanvirahmedodesk

1 answer

locus of the point of intersection of tangent to $y^2=4ax$ which intercept a constant length d on the directrix

asked Jan 17, 2015 by tanvirahmedodesk

1 answer

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.

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

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

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

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

asked Oct 17, 2014 by sreemathi.v

1 answer

The length of the latus rectum of the ellipse $3x^2+y^2=12$ is

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

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

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

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

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

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

asked Oct 16, 2014 by sreemathi.v

1 answer

Equation of a circle which passes through $(3,6)$ and touches the axes is

asked Oct 16, 2014 by sreemathi.v

1 answer

The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is

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 ___

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 _________

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 ____________

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 ____________

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 _____________

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 __________

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.

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 $(3,2)$

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 $PS+PS'=8$.

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 $ln=am^2$

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 $x^2+y^2-2x+6y+1=0$.

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.

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 $5$.

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 $x^2+y^2+6x+2y=0$.

asked Oct 15, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with foci $(0,\pm\sqrt{10})$,passing through $(2,3)$.

asked Oct 15, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with vertices $(0,\pm 7),e=\large\frac{4}{3}$.

asked Oct 15, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with vertices $(\pm 5,0)$,foci $(\pm 7,0)$.

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.

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 $y = 9$.

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.

asked Oct 14, 2014 by sreemathi.v

1 answer

Find the equation of the following parabola : Focus at $(-1,-2)$,directrix $x-2y+3=0$.

asked Oct 14, 2014 by sreemathi.v

1 answer

Find the equation of the following parabola : Vertex at $(0,4)$,focus at $(0,2)$.

asked Oct 14, 2014 by sreemathi.v

1 answer

Find the equation of the following parabola : Directrix $x=0$,focus at $(6,0)$.

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 $y=x-1$.

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 $(5,5)$.

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 $2x-5y+18=0$.

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 $y-4x+3=0$.

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.

asked Oct 13, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm 2,0)$.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the eccentricity of the hyperbola $9y^2-4x^2=36$.

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.

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 $m$.

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.

asked Oct 10, 2014 by sreemathi.v

1 answer

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