Question

How do you find the center – radius form of the equation of the circle given center (0, -2) , radius 6?

Answer 1

Hint: To do this, first you need to write the formula for the equation of the circle in the radius form. The formula for the equation of the circle is $\left(x-x_1\right)^2+\left(y-y_1 \right)^2 = r^2$ . Here the variables $x_1$ and $y_1$ are the coordinates of the circle. So according to the questions, the variables should be 0 for the x co - ordinate and -2 for the y co – ordinate. Also, the r in the equation is the radius. In the question, the given value for the radius is 6, so you should substitute it to get the equation.

Complete step by step answer:
Here is the complete step by step solution.
The first step is to write the formula for the equation of the circle in the radius form.
The formula for the equation of the circle is given by
 $\left(x-x_1\right)^2+\left(y-y_1 \right)^2 = r^2$
The next step is to find out the variables. Here the variables $x_1$ and $y_1$ are the coordinates of the circle. So according to the questions, the variables should be 0 for the x co - ordinate and -2 for the y co – ordinate.
Next step is to substitute r for the radius of the circle. In the question, the radius is given as 6. Therefore, substituting all the values, we get the equation of the circle a s
$\Rightarrow \left(x\right)^2+\left(y+2 \right)^2 = 6^2$
$\Rightarrow \left(x\right)^2+\left(y+2 \right)^2 = 36$

Therefore, the answer for the question is $ \left(x\right)^2+\left(y+2 \right)^2 = 36$

Note: You need to know the formulas for the equations of various shapes like the circle , parabola, hyperbola. Also it is important to remember the formulas for the normal and tangent for different shapes, such as parabola, circle, hyperbola, and also the ellipse.