The equation $x^2 + y^2 - 2x + 4y - 4 = 0$ represents a circle whose radius is:

Question

Accepted Answer

Comparing with $x^2 + y^2 + 2gx + 2fy + c = 0$, we get $2g = -2 \Rightarrow g = -1$, $2f = 4 \Rightarrow f = 2$, and $c = -4$. Radius $r = \sqrt{g^2 + f^2 - c} = \sqrt{(-1)^2 + 2^2 - (-4)} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3$.

Conic Sections

❓ Sibling Questions in this Chapter