First slide

Parabola

Question

Two straight lines are perpendicular to each other. One of them touches the parabola $y^{2} = 4 a (x + a)$ and the other touches $y^{2} = 4 b (x + b)$ .Their point of intersection lies on the line

Moderate

A

$x - a + b = 0$
B

$x + a - b = 0$
C

$x + a + b = 0$
D

$x - a - b = 0$

Solution

Given parabola is $y^{2} = 4 a (x + a)$
Slope form of equation of tangent is $y = m (x + a) + \frac{a}{m}$ …..(i)
$Any tangent to y^{2} = 4 b (x + b) which is perpendicular to (i) is y = - \frac{1}{m} (x + b) - b m \dots (ii)$
Subtracting (i) & (ii),
$\begin{array}{l} we get (m + \frac{1}{m}) x + (a + b) (m + \frac{1}{m}) = 0 \\ \Rightarrow x + a + b = 0 \end{array}$
Which is a locus of their point of intersection.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App