Question

If the segment intercepted by the parabola $y^2=4ax$ with the line $lx+my+n=0$ subtends a right angle at the vertex, then

• A. $4al+n=0$
• B. $4al+4am+n=0$
• C. $4am+n=0$
• D. $al+n=0$

Answer 1

The correct option is A $4al+n=0$

Given:

Parabola, $P:y^2=4ax$

Line, $L:lx+my+n=0$

From line, we get

$1=-\frac{lx+my}{n}$

Using this in homogenising the parabolic equation, we get

$y^2=4ax(-\frac{lx+my}{n})$

Since, the line $L$ subtends right angle at origin, therefore,

Coefficient of $x^2+$ Coefficient of $y^2$ =0

$\Rightarrow 4al+n=0$

Hence, option A.