The solution of \$frac{{dy}}{{dx}} = \frac{{ax + h}}{{by + k}}$ represents a parabola

The equation $y^2+3 =2( 2x +y)$ represents a parabola with vertex at 

If the equation of parabola is ${x}^{2}=-9y$, then the equation of the directrix and the length of latus rectum are 

If $\displaystyle \left ( 2,0 \right )$ is the vertex and $y -$ axis the directrix of a parabola,find the coordinates of focus. 

The focal distance of a point $P$ on the parabola $y^2=12x$ if the ordinate of $P$ is $6$, is

The equation of the conic with focus $\displaystyle S \left( \frac{3}{2}, 0 \right) $ and the directrix 2x + 3 = 0 having eccentricity 1, is

The locus of the points which are equidistant from $(-a, 0)$ and $x=a$ is

Find the equation of the parabola whose focus is $S(3,5)$ and vertex is $A(1,3)$.

eccentricity of the conic $25x^2-9y^2 = 225$, are

The equation $(13x - 1)^{2} + (13y - 1)^{2} = k(5x - 12y + 1)^{2}$ will represent a parabola if

If the eqn of directrix to the parabola $x^{2}+4y-6x+\lambda=0$ is $y+1=0$, then 

The focus of the parabola $y ^ { 2 } = 4 y - 4 x$ is

Equation of the directrix of the parabola whose focus is $(0,0)$ and the tangent at the vertex is $x-y+1=0$ is 

The equation of the directrix of the parabola, $y ^ { 2 } + 4 y + 4 x + 2 = 0$ is -

The equation of directrix of the parabola $(y-2)^{2}=4(x-4)$, is

The vertex of the parabola $ {4y}^{2} + 12x-12y+39= 0$ is:

The focus of the parabola $(y-2)^{2}=20(x+3)$ is:

A parabola is written as $x^{2}=4ay$, its focus and equation of the directrix is:

Focus of the parabola $4x^{2}-12x+8y+13=0$ is

The locus of the foot of the perpendicular from the focus upon a tangent to the parabola $y^{2}=4ax$ is 

Maximum radius of the circle inscribed in parabola ${y}^{2}=4x$ with centre its focus is ..

The locus of the midpoint of the line segment joining the focus to a  moving point on the parabola y$^2$ - 4ax is another parabola with directrix

Equation of the directrix of the parabola $4y^2-6x-4y-5=0$ is 

The equation of the directrix of the parabola $y= x^2-2x+3$ is 

The focus of the parabola $x^2 -4x+2y+8=0$ is 

The equation of the directrix of the parabolas $x=-2at,\ y=-at^{2},\ t\ \epsilon \ R$ is

The angle of intersection at the origin to the curves ${ y }^{ 2 }=4x$ and ${ x }^{ 2 }=4y$ is :

if the vertex and the focus of the parabola are $(-1, -1) & (2, 3)$ respectively, then the equation of the directrix is

The parametric equation of a parabola is $x=t^{2}+1, y=2t+1$. The Cartesian equation of its directrix is 

$TP$ and $TQ$ are tangents to parabola $y^{2}=4x$ and normal at $P$ and $Q$ intersect at a point $R$ on the curve. The locus of the center of the circle circumscribing $\Delta TPQ$ is parabola whose

For parabola $x^{ 2 } + y^{ 2 } + 2xy 6x 2y + 3 = 0$ the focus is

The vertex of the parabola $2((x-1)^2 + (y-2)^2) = (x + y + 3)^2$ is

If a point $\mathrm{P}$ moves such that the distance from the point $\mathrm{A} (1, 1)$ and the line $x+y+2=0$ are equal then the locus of $\mathrm{P}$ is equal to

If the vertex of the conic $y^{2} - 4y = 4x - 4a$ always lies between the straight lines $x + y = 3$ and $2x + 2y - 1 = 0$ then

For the parabola $9x^{2} - 24xy + 16y^{2} - 20x - 15y - 60 = 0$ which of the following is/ are true.

Two manually perpendicular tangent of the parabola ${ y }^{ 2 }=4ax$ meet the axis in ${P} _{1}$ and ${P} _{2}$. If $S$ is the focus of the parabola, then $\dfrac { 1 }{ \left( S{ P } _{ 1 } \right)  } +\dfrac { 1 }{ \left( S{ P } _{ 2 } \right)  } $ is equal to :-

A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.

The equation of a parabola in its standard form is $x^3=4ay.$

The ratio in which the line segment joining the points $(4, -6)$ and $(3, 1)$ is divided by the parabola $y^2 = 4x$ is

Each member of the family of parabolas $y=ax^2+2x+3$ has a maximum or a minimum point depending upon the value of $a$. The equation of the locus of the maxima or minima for all possible values of $a$ is

The focus of the parabola $y=2x^{2}+x$ is

If the vertex and the focus of a parabola are $\left (-1,1 \right )$ and $\left (2,3 \right )$ respectively, then the equation of the directrix is

The axis of the conic $\displaystyle x^{2}+4y-6x+17=0$ is

The equation of directrix from the following is,

The equation of pair of tangents to a parabola is given by $3x^2 +4y^2 +7xy -2x -y - 5 =0 $ and its focus is (1, 1), then the equation of directrix of the parabola is given by