Finding the center, radius of a circle when there is a constant in front of the variables

Question

$$4x^2+(y-2)^2 = 4$$

How to find the center and radius of a circle when there is a constant in front of the variables?

Answer 1

As Eevee Trainer commented, this is an ellipse

You can rewrite the equation as $$\frac{(x-0)^2}{1^2} + \frac{(y-2)^2}{2^2} = 1$$

which suggests that

• the centre of the ellipse is at $(0,2)$
• the semi-minor axis (an equivalent of the radius) parallel to the $x$-axis is $1$
• the semi-major axis (the other equivalent of the radius) parallel to the $y$-axis is $2$