The radius of the circle whose centre is `(-4,0)` and which cuts the parabola `y^(2)=8x` at A and B such that the common chord AB subtends a right angle at the vertex of the parabola is equal to

Options

A. `4sqrt(13)`
B. `3sqrt(5)`
C. `3sqrt(2)`
D. `2sqrt(5)`

Answer

A

Explanation

(1) As shown in the figure, common chord AB subtends right angle at vertex.

Slope of `OA=(4t-0)/(2t^(2)-0)=45^(@)`
`rArr" "(2)/(t)=trArrt=2`
`A-=(8,8)`
So, radius of circle = CA
`=sqrt((8+4)^(2)+(8-0)^(2))`
`=sqrt(144+64)`
`=4sqrt(13)`