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The extremities of the diagonal of a rec...

The extremities of the diagonal of a rectangle are `(-4, 4)` and `(6,-1)`. A circle circumscribes the rectangle and cuts inercept of length `AB` on the `y`-axis. The length of `AB` is

A

`11`

B

`12`

C

`13`

D

`14`

Text Solution

Verified by Experts

The correct Answer is:
A
Since circle circumscribes the rectangle and so the its diagonal with vertices `(-4,4)` and `(6,-1)` will act as diameter of the circle. Hence its equation is
`implies(x+4)(x-6)+(y-4)(y+1)=0`
`impliesx^(2)+y^(2)-2x-3y-2=0`
length of `AB=2sqrt((3/2)^(2)+28)=11`
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