Question

Find the length of tangent of parabola $y^2=8x$ at $(2,4)$.

(Length of the tangent of a parabola is defined as the distance between the point of the contact and the $x$-intercept of the tangent)

• A. $4\sqrt{2}$
• B. $4\sqrt{3}$
• C. $3\sqrt{4}$
• D. None of these

Answer 1

The correct option is A $4\sqrt{2}$

$y^2=8x$

$\therefore \frac{dx}{dy}=\frac{y}{4}$

Length of tangent $=\left|y\sqrt{1+(\frac{dx}{dy}{)}^2}\right|$

$=\left|y\sqrt{1+(\frac{y}{4}{)}^2}\right|$

So, the length of tangent at $(2,4)=\left|4\sqrt{1+(\frac{4}{4}{)}^2}\right|=4\sqrt{2}units$

So, the answer is option (A).