Question

The pole of the line $2 x = y$with respect to the parabola $y ^ { 2 } = 2 x$ is

• A. $\left( 0 , \frac { 1 } { 2 } \right)$
• B. $\left( \frac { 1 } { 2 } , 0 \right)$
• C. $\left( 0 , - \frac { 1 } { 2 } \right)$
• D. None

Answer 1

Answer: (A)

$\left( 0 , \frac { 1 } { 2 } \right)$

Answer 2

Let $2 x = y$ w.r.t. parabola $y ^ { 2 } = 2 x$ its polar is $y y _ { 1 } = x + x _ { 1 }$

Also polar is $\left( 0 , \frac { 1 } { 2 } \right)$