Question

The equation of tangent to parabola $y^2=32x$ at ends of its latus rectum is

• A. $x-y+8=0$
• B. $x+y+8=0$
• C. $x+y-8=0$
• D. both (1) and (2)

Answer 1

Answer: (D)

both (1) and (2)

Given parabola is $y^2=32x$
So the end points of latus rectum are $(a,\pm 2a)=(8,\pm 16)$
Thus equation of tangent at these points are given by,$T=0$
$\Rightarrow (\pm 16)y=32\left(\frac{x+8}{2}\right)$
$\Rightarrow \pm y=x+8$
$\Rightarrow x+y+8=0$ & $x-y+8=0$