Question

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola $y ^ { 2 } = 8 x$ is

• A. $\frac { 1 } { 2 } \sqrt { 41 }$
• B. $\sqrt { 41 }$
• C. $\frac { 3 } { 2 } \sqrt { 41 }$
• D. $2 \sqrt { 41 }$

Answer 1

Answer: (C)

$\frac { 3 } { 2 } \sqrt { 41 }$

Answer 2

Equation of chord of contact of tangents drawn from a point $\left( x _ { 1 } , y _ { 1 } \right)$to parabola $y ^ { 2 } = 4 a x$is $y y _ { 1 } = 2 a \left( x + x _ { 1 } \right)$. So that

$5 y = 2 \times 2 ( x + 2 )$⇒ $5 y = 4 x + 8$.

Point of intersection of chord of contact with parabola $y ^ { 2 } = 8 x$are $\frac { 3 } { 2 } \sqrt { 41 }$