Trigonometry Examples

Find the Center and Radius 9=2y-y^2-6x-x^2
Step 1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
Divide both sides of the equation by .
Step 3
Complete the square for .
Tap for more steps...
Step 3.1
Reorder and .
Step 3.2
Use the form , to find the values of , , and .
Step 3.3
Consider the vertex form of a parabola.
Step 3.4
Find the value of using the formula .
Tap for more steps...
Step 3.4.1
Substitute the values of and into the formula .
Step 3.4.2
Cancel the common factor of and .
Tap for more steps...
Step 3.4.2.1
Factor out of .
Step 3.4.2.2
Cancel the common factors.
Tap for more steps...
Step 3.4.2.2.1
Factor out of .
Step 3.4.2.2.2
Cancel the common factor.
Step 3.4.2.2.3
Rewrite the expression.
Step 3.4.2.2.4
Divide by .
Step 3.5
Find the value of using the formula .
Tap for more steps...
Step 3.5.1
Substitute the values of , and into the formula .
Step 3.5.2
Simplify the right side.
Tap for more steps...
Step 3.5.2.1
Simplify each term.
Tap for more steps...
Step 3.5.2.1.1
Raise to the power of .
Step 3.5.2.1.2
Multiply by .
Step 3.5.2.1.3
Cancel the common factor of .
Tap for more steps...
Step 3.5.2.1.3.1
Cancel the common factor.
Step 3.5.2.1.3.2
Rewrite the expression.
Step 3.5.2.1.4
Multiply by .
Step 3.5.2.2
Subtract from .
Step 3.6
Substitute the values of , , and into the vertex form .
Step 4
Substitute for in the equation .
Step 5
Move to the right side of the equation by adding to both sides.
Step 6
Complete the square for .
Tap for more steps...
Step 6.1
Reorder and .
Step 6.2
Use the form , to find the values of , , and .
Step 6.3
Consider the vertex form of a parabola.
Step 6.4
Find the value of using the formula .
Tap for more steps...
Step 6.4.1
Substitute the values of and into the formula .
Step 6.4.2
Cancel the common factor of and .
Tap for more steps...
Step 6.4.2.1
Factor out of .
Step 6.4.2.2
Cancel the common factors.
Tap for more steps...
Step 6.4.2.2.1
Factor out of .
Step 6.4.2.2.2
Cancel the common factor.
Step 6.4.2.2.3
Rewrite the expression.
Step 6.4.2.2.4
Divide by .
Step 6.5
Find the value of using the formula .
Tap for more steps...
Step 6.5.1
Substitute the values of , and into the formula .
Step 6.5.2
Simplify the right side.
Tap for more steps...
Step 6.5.2.1
Simplify each term.
Tap for more steps...
Step 6.5.2.1.1
Raise to the power of .
Step 6.5.2.1.2
Multiply by .
Step 6.5.2.1.3
Divide by .
Step 6.5.2.1.4
Multiply by .
Step 6.5.2.2
Subtract from .
Step 6.6
Substitute the values of , , and into the vertex form .
Step 7
Substitute for in the equation .
Step 8
Move to the right side of the equation by adding to both sides.
Step 9
Simplify .
Tap for more steps...
Step 9.1
Add and .
Step 9.2
Add and .
Step 10
Reorder terms.
Step 11
This is the form of a circle. Use this form to determine the center and radius of the circle.
Step 12
Match the values in this circle to those of the standard form. The variable represents the radius of the circle, represents the x-offset from the origin, and represents the y-offset from origin.
Step 13
The center of the circle is found at .
Center:
Step 14
These values represent the important values for graphing and analyzing a circle.
Center:
Radius:
Step 15