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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

A. `4sqrt(13)`

B

B. `3sqrt(5)`

C

C. `3sqrt(2)`

D

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. An equilateral triangle is inscribed in the parabola y^(2)=4ax, such...

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  8. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

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  16. Two parabola have the same focus. If their directrices are the x-axis ...

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