# If the circle has a radius of 3 units and the center lies on the y-axis, which set of values of A, B, C, D, and E might correspond to the circle in general form?

Jun 1, 2017

The general form for a conic section is:

$A {x}^{2} + B x y + C {y}^{2} + D x + E y + F = 0$

For a circle we know that $A = C$ and $B = 0$. The most likely values are $A = C = 1$

The phrase; "the center lies on the y-axis" tells us that the x coordinate of the center is 0 and, therefore, $D = 0$

We can infer nothing about E, except $E \in \mathbb{R}$

Also, the phrase; "the circle has a radius of 3 units" tells us that $\frac{F}{A} = - 9$