Question

The difference of the squares of the perpendicular drawn from the points $(a\pm k,0)$ on any tangent to the parabola $y^2=4ax$ is

• A. $4$
• B. $4a$
• C. $4k$
• D. $4ak$

Answer 1

Answer: (D)

$4ak$

Equation any tangent to the parabola $y^2=4ax$ is

$ty=x+{at}^2$ ...(1)

The difference of the squares of the perpendiculars from $(a\pm k,0)$ to (1) is

$\frac{{(a+k+a{t}^2)}^2-{(a-k+a{t}^2)}^2}{1+t^2}=\frac{4a(1+t^2)k}{1+t^2}=4ak$