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Question

Values of p and q for which equation (x+y−41)2−(x+7y−7)(px+qy+1)=0 represents a circle are

A
p=7/25, q=1/25
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B
p=7/25, q=1/25
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C
p=1/25, q=7/25
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D
p=1/25, q=7/25
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Solution

The correct option is B p=7/25, q=1/25
On expanding, the equation becomes
(1p)x2+(17q)y2+(2q7p)xy+(821+7p)x+(827+7p)y+1688=0
Now, we equate the coefficients of x2 and y2 also of x and y, and make the coefficient of xy=0 since the equation represents a circle.
Hence,
1p=17q
2q7p=0
On solving we get,
p=725, q=125

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