Q66 / 180 · COMEDK 2023 (Memory Based) · Mathematics

The circle $x^2+y^2+3 x-y+2=0$ cuts an intercept on $X$-axis of length

  • A
    3
  • B
    4
  • C
    2
  • Correct answer
    D
    1

Solution

Given equation of circle is $x^2+y^2+3 x-y+2=0$. On comparing this equation with $x^2+y^2+2 g x+2 f y+c=0$, we get $g=\frac{3}{2}, f=-\frac{1}{2}$ and $c=2$ Now, the length of intercept on $\mathrm{X}$-axis $=2 \sqrt{g^2-c}$ $=2 \sqrt{\left(\frac{3}{2}\right)^2-2}=2 \sqrt{\frac{9}{4}-2}=2 \sqrt{\frac{1}{4}}=2\left(\frac{1}{2}\right)=1$

Hence, the correct answer is option: 'D'.

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