Q90 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

If the equation $a x^2+b y^2+2 h x y+2 g x+2 f y+c=0$ represents a circle passing through the origin, then

  • A
    $a=b, c=0$
  • B
    $|a|=|b|, h=0=c$
  • Correct answer
    C
    $a=b, h=c=0$
  • D
    $a=b, h=0$

Solution

The standard equation of circle which passes through origin is $x^2+y^2+2 g x+2 f y=0$ If the equation $a x^2+b y^2+2 h x y+2 f y+c=0$ represent a circle passing through origin, then $a=b, h=0, c=0$.

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

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