Question

If the curve y = | x- 3| touches the parabola $y^2=\lambda (x-4),\lambda >0$, then latus rectum of the parabola, is

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

The correct option is B 4

$y^2=\lambda (x-4)$

The basic equation of parabola:

$(y-k{)}^2=4a(x-h)$

$\Rightarrow (h,k)=(4,0)$

As latus rectum of parabola is given by the equation: $|4a|$

$\Rightarrow 4a=\lambda$

Considering $a=1\Rightarrow \lambda =4$

$\therefore \lambda =4$