Trigonometry Examples

$9.5 = 4 {(x - 2)}^{2} + 4 {(y - 3)}^{2}$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 {(x - 2)}^{2} + 4 {(y - 3)}^{2} = 9.5$

Step 2

Divide both sides of the equation by $4$ .

${(x - 2)}^{2} + {(y - 3)}^{2} = 2.375$

Step 3

This is the form of a circle. Use this form to determine the center and radius of the circle.

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Step 4

Match the values in this circle to those of the standard form. The variable $r$ represents the radius of the circle, $h$ represents the x-offset from the origin, and $k$ represents the y-offset from origin.

$r = \sqrt{2.375}$

$h = 2$

$k = 3$

Step 5

The center of the circle is found at $(h, k)$ .

Center: $(2, 3)$

Step 6

These values represent the important values for graphing and analyzing a circle.

Center: $(2, 3)$

Radius: $\sqrt{2.375}$

Step 7