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JEE Main 2009

Exam: JEE Main
Year: 2009
Subject: Mathematics
Chapter: Circle

JEE Main 2009 · Mathematics · Circle

If P and Q are the points of intersection of the circles x^2+y^2+3...

If

P

and

Q

are the points of intersection of the circles

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

and

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

, then there is a circle passing through

P, Q

and

(1,1)

for

Options

Aall values of $p$
Ball except one value of $p$
Call except two values of $p$
Dexactly one value of $p$

Correct answer

A. all values of $p$

Step-by-step solution

Given circles

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

S^{\prime}=x²+y²+2 x+2 y-p²=0 Equation of required circle is

S+\lambda S^{\prime}=0

As it passes through

(1,1)

the value of

\lambda=\frac{-(7+2 p)}{\left(6-p^2\right)}

If

7+2 p=0

, it becomes the second circle

\therefore

it is true for all values of

p

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