$y^{2} = 4 a x$ be the equation of a parabola, then

Open in App

Solution

For the parabola $y^{2} = 4 a x$ ,
A) Equation of the tangent at $(x_{1}, y_{1})$ is $y y_{1} = 2 a (x + x_{1})$
B) Equation of the normal at $(x_{1}, y_{1})$ is $y - y_{1} = - \frac{y_{1}}{2 a} (x - x_{1})$
$\Rightarrow$ $x y_{1} = 2 a (y_{1} - y) + x_{1} y_{1}$
C) Equation of the focal chord through $(x_{1}, y_{1})$ and focus $(a, 0)$ is
$y = \frac{y_{1} - 0}{x_{1} - a} (x - a) \Rightarrow x y_{1} = y (x_{1} - a) + a y_{1}$
D) Equation of the line joining $(- a, 0)$ , the point of intersection of the axis $y = 0$ and the directrix $x + a = 0$ with $(x_{1}, y_{1})$ is $(x + a) y_{1} = (x_{1} + a) y$

Suggest Corrections

Similar questions

Find the equation of tangent to parabola $y^{2} = 4 a x a t (a t^{2}, 2 a t)$

Q. If

x = 2

is the equation of the directrix of the parabola

y^{2} = - 4 a x

, then the focus of the parabola is

Q. Find the equations to the common tangents of the circle

x^{2} + y^{2} + 4 a x = 0

and parabola

y^{2} = 4 a x .

Q. Let

y^{2} = 4 a x

be a parabola and

x^{2} + y^{2} + 2 b x = 0

be a circle. If parabola and circle touch each other externally then:

If normal at p to parabola $y^{2} = 4 a x$ meets parabola again at Q such that PQ subtends a right angle at the vertex of $y^{2} = 4 a x$ then p will be

Join BYJU'S Learning Program

y2=4ax be the equation of a parabola, then

$y^{2} = 4 a x$ be the equation of a parabola, then