Question

$a{x}^2+2y^2+2bxy+2x-y+c=0$ 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
• D. a = 2, b = 0, c = 0

Answer 1

The correct option is D a = 2, b = 0, c = 0

We know the condition for a second degree curve to be a circle which is, a = b and h = 0
which gives us a = 2, b = 0
Also here, we have to check the condition for circle to pass through origin i.e. origin satisfies equation of circle or c = 0.