Q 1. - Calculus

Question

Finding the center and radius for a circle by completing the square:

Each of the equations that follow is an equation for a circle.

Find the center and radius for each.

$x^2+y^2-y-\frac{3}{4}=0$

Step-by-Step Solution

Answer

Center is $\left(0,\frac{1}{2}\right)$ and radius is equal to 1 unit.

Step 1. Given information

An equation of a circle is $x^2+y^2-y-\frac{3}{4}=0$

Step 2. Explanation

$\begin{array}{rcl}{x}^2+y^2-y-\frac{3}{4}& =& 0\\ x^2+y^2-2\left(\frac{1}{2}\right)y+{\left(\frac{1}{2}\right)}^2-{\left(\frac{1}{2}\right)}^2-\frac{3}{4}& =& 0\\ x^2+{\left(y-\frac{1}{2}\right)}^2& =& 1\end{array}$

So, center is $\left(0,\frac{1}{2}\right)$ and radius is 1 unit.