Question

# Find the equation of director circle of the circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

A

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B

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C

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D

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Solution

## The correct option is D Diameter of give circles 2x-3y+12=0 .............(1) x+4y-5=0 .............(2) Intersection point of these two diameter will give us the centre of circle. solving equation 1 & 2. multiply 2 in equation (2) and substarct it from equation (1) x=-3,y=2 Center of the circle (-3,2) Given area of circle =154 πr2=154 227×r2=154 r=7 The director circle of a circle is the concentric circle having radius equal to √2 times the original circle center of director circle (-3,2) Radius of director circle =√2×7 (x+3)2+(y−2)2=(√2×7)2 (x+3)2+(y−2)2=98 x2+9+6x+y2+4−4y=98 x2+y2+6x−4y−85=0 Option D is correct

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