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The radius of the circle whose centre is...

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

A

`4sqrt(13)`

B

`3sqrt(5)`

C

`3sqrt(2)`

D

`2sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
(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)`
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  7. If the normals to the parabola y^2=4a x at P meets the curve again at ...

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  11. The endpoints of two normal chords of a parabola are concyclic. Then ...

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  14. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

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