Q90 / 160 · TS EAMCET 2024 (11 May Shift 1) · Mathematics
The line $x+y+1=0$ intersects the circle $x^2+y^2-4 x+2 y-4=0$ at the points A and B. If $M$ $(a, b)$ is the midpoint of AB , then $a-b=$
- A$0$
- B$1$
- C$2$
- Correct answerD$3$
Solution
$x+y+1=0 \Rightarrow y=-x-1$
Solving for point of intersection $\begin{aligned} & x^2+(-x-1)^2-4 x+2(-x-1)-4=0 \\ & 2 x^2-4 x-5=0 ; x_1+x_2=2 \Rightarrow \frac{x_1+x_2}{2}=a=1 \\ & a+b+1=0 \Rightarrow b=-2 \therefore a-b=3 \end{aligned}$
Solving for point of intersection $\begin{aligned} & x^2+(-x-1)^2-4 x+2(-x-1)-4=0 \\ & 2 x^2-4 x-5=0 ; x_1+x_2=2 \Rightarrow \frac{x_1+x_2}{2}=a=1 \\ & a+b+1=0 \Rightarrow b=-2 \therefore a-b=3 \end{aligned}$
Hence, the correct answer is option: 'D'.