Q66 / 180 · COMEDK 2024 (Memory Based) · Mathematics
The length of $y$-intercept of the circle $x^2+y^2-6 x+4 y+3=0$ is
- Correct answerA2
- B$2 \sqrt{2}$
- C$2 \sqrt{7}$
- D$2 \sqrt{6}$
Solution
General equation of circle is
$x^2+y^2+2 g x+2 f y+c=0$
On comparing with given equation $x^2+y^2-6 x+4 y+3=0$, we get
$\begin{aligned}<br/>g & =-3 \\<br/>f & =2 \\<br/>c & =3 \\<br/>y \text {-intercept } & =2 \sqrt{f^2-c} \\<br/>& =2 \sqrt{4-3}=2 \sqrt{1}=2<br/>\end{aligned}$
$x^2+y^2+2 g x+2 f y+c=0$
On comparing with given equation $x^2+y^2-6 x+4 y+3=0$, we get
$\begin{aligned}<br/>g & =-3 \\<br/>f & =2 \\<br/>c & =3 \\<br/>y \text {-intercept } & =2 \sqrt{f^2-c} \\<br/>& =2 \sqrt{4-3}=2 \sqrt{1}=2<br/>\end{aligned}$
Hence, the correct answer is option: 'A'.