First slide

Definition of a circle

Question

The equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ represents a circle, the condition will be

Moderate

A

$a = b$ and $c = 0$
B

$f = g$ and $h = 0$
C

$a = b$ and $h = 0$
D

$f = g$ and $c = 0$

Solution

Comparing $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ with $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ we find that the given equation will represent a circle if $a = b$ and $h = 0$

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