If P and Q are the points of intersection of the circles x²+ y²+ 3x + 7y + 2p – 5 = 0 and x²+ y²+ 2x + 2y – p² = 0, then there is a circle passing through P, Q and (1, 1) for

all values of p

all except one value of p

all except two values of p

exactly one value of p

Solution

all except one value of p

Radical axis is x + 5y + p2 + 2p – 5 =0
Equation of circle is
x² + y² + 3x + 7y + 2p – 5 + λ [x + 5y + p² + 2p – 5 ] = 0 …. (i)
(i) passes through (1, 1)
$rightwards double arrow space straight lambda space equals negative space fraction numerator left parenthesis 2 straight p space plus 7 right parenthesis over denominator left parenthesis straight p plus 1 right parenthesis squared end fraction space space space space space space space space space space space space space space left parenthesis straight p space not equal to negative 1 right parenthesis$

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Three Dimensional Geometry

If P and Q are the points of intersection of the circles x²+ y²+ 3x + 7y + 2p – 5 = 0 and x²+ y²+ 2x + 2y – p² = 0, then there is a circle passing through P, Q and (1, 1) for

all values of p

all except one value of p

all except two values of p

exactly one value of p

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

If P and Q are the points of intersection of the circles x2+ y2+ 3x + 7y + 2p – 5 = 0 and x2+ y2+ 2x + 2y – p2 = 0, then there is a circle passing through P, Q and (1, 1) for all values of p all except one value of p all except two values of p exactly one value of p

Some More Questions From Three Dimensional Geometry Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If P and Q are the points of intersection of the circles x²+ y²+ 3x + 7y + 2p – 5 = 0 and x²+ y²+ 2x + 2y – p² = 0, then there is a circle passing through P, Q and (1, 1) for

all values of p

all except one value of p

all except two values of p

exactly one value of p