JEE MATHEMATICS MCQ: SYSTEM OF CIRCLES

1 Easy

1 of 1

Analyzing +4 | -1

P

and

Q

are the points of intersection of the circles

{x^2} + {y^2} + 3x + 7y + 2p - 5 = 0

{x^2} + {y^2} + 2x + 2y - {p^2} = 0

, then there is a circle passing through

P,Q

and

\left( {1,1} \right)

and

View answer and explanation

Correct option: B

All except one value of

p

Option B (All except one value of

p

) is correct because there is a circle passing through P, Q, and (1,1) for all values of p except when the equation becomes undefined.

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x = 1

{x^2} + {y^2} = 4

{x^2} + {y^2} + 8y - 4 = 0

{x^2} + {y^2} + gx + 4 = 0

x^2+y^2+3 x+2 y+1=0

x^2+y^2+3 x+4 y+2=0

{x^2} + {y^2} + 2ky + 2x + 6 = 0

{x^2} + {y^2} + 2ky + k = 0

k

x^2+y^2+2 a x+c y+a=0

x^2+y^2-3 a x+d y-1=0

P

Q

5 x+b y-a=0

P

Q

x + 2y - 3 = 0

{x^2} + {y^2} - 4y + 1 = 0

{x^2} + {y^2} - 4x - 2y + 4 = 0