Analytical geometry - circles

Question

How do you find the point for a circle and find the radiums when x squared has a co-efficient?

Answer 1

For an equation of the form $$ax^2 + by^2 = c^2$$ unless $a = b$, you do not have a circle, but rather, an ellipse.

If $a = b$, then you do have a circle, and you can rewrite your equation as $$x^2 + y^2 = \left(\frac ca\right)^2\tag{1}$$

In this case $(1)$, the center of the circle is the origin, and the radius is $\dfrac ca$.

In general, the equation of a circle with center $(x_0, y_0)$ and radius $r$ is given by:$$(x- x_0)^2 + (y-y_0)^2 = r^2$$