Question

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?

Answer 1

The general form for a conic section is:

`Ax^2+Bxy + Cy^2 + Dx + Ey + 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 RR`

Also, the phrase; "the circle has a radius of 3 units" tells us that `F/A=-9`