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Circle Inscribing a Triangle Fromed by 3 Given Lines

The lines 2 x...

Question

The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 square units. The equation of the circle is

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 B

Centre of circle = Point of intersection of diameters =(1,-1)
Now area =154 $\Rightarrow π r^{2} = 154 \Rightarrow r = 7$
Hence the equation of required circle is
$(x - 1)^{2} + (y + 1)^{2} = 7^{2} \Rightarrow x^{2} + y^{2} - 2 x + 2 y = 47$

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