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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Circle

Let the circle C_1: x^2+y^2-2(x+y)+1=0 and C_2 be a circle having...

Let the circle C1:x2+y2−2(x+y)+1=0C_1: x^2+y^2-2(x+y)+1=0 and C2C_2 be a circle having centre at (−1,0)(-1,0) and radius 2 . If the line of the common chord of C1\mathrm{C}_1 and C2\mathrm{C}_2 intersects the yy-axis at the point P\mathrm{P}, then the square of the distance of P\mathrm{P} from the centre of C1\mathrm{C}_1 is :

Options

  1. A2
  2. B1
  3. C4
  4. D6

Correct answer

A. 2

Step-by-step solution

S1:x2+y2−2x−2y+1=0S2:x2+y2+2x−3=0 Common chord =S1−S2=0−4x−2y+4=02x+y=2⇒P(0,2)d(c,p)2=(1−0)2+(2−1)2=2\begin{aligned} & S_1: x^2+y^2-2 x-2 y+1=0 \\ & S_2: x^2+y^2+2 x-3=0 \\ & \text{ Common chord }=S_1-S_2=0 \\ & -4 x-2 y+4=0 \\ & 2 x+y=2 \Rightarrow P(0,2) \\ & d_{(c, p)}^2=(1-0)^2+(2-1)^2=2\end{aligned}
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