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A rhombus is inscribed in the region com...

A rhombus is inscribed in the region common to the two circles `x^2+y^2-4x-12=0` and `x^2+y^2+4x-12=0` with two of its vertices on the line joining the centers of the circles. The are of the rhombus is `8sqrt(3)s qdotu n i t s` (b) `4sqrt(3)s qdotu n i t s` `6sqrt(3)s qdotu n i t s` (d) none of these

A

`8 sqrt(3)` sq. units

B

`4 sqrt(3)` sq. units

C

`6 sqrt(3)` sq. units

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1

The circles are with centers (2,0) and `(-2,0)` and radius 4.
Therefore, the y-axis is their common chord.
`Delta ABC` is equilateral. Hence,
Area of ADBC `=(2xxsqrt(3))/(4)(4)^(2)=8sqrt(3)`
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CENGAGE-CIRCLE -Exercise (Single)
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