a x^2 + 2 y^2 + 2bxy + 2x - y + c = 0 represents a circle through… - Vidyadip

MCQ

$a{x^2} + 2{y^2} + 2bxy + 2x - y + c = 0$ represents a circle through the origin, if

A
$a = 0,\;b = 0,\;c = 2$
B
$a = 1,\;b = 0,\;c = 0$
C
$a = 2,\;b = 2,\;c = 0$
✓
$a = 2,\;b = 0,\;c = 0$

✓

Answer

Correct option: D.

$a = 2,\;b = 0,\;c = 0$

d
(d) See condition for circle and also condition for circle to pass through origin

$i.e.$ origin satisfies equation of circle or $c = 0$.

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