91Ó°ÊÓ

Write an equation of the circle with the given center and radius. See Example 8. $$ (-7,6) ; 2 $$

Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ \frac{(x-1)^{2}}{49}+\frac{(y+2)^{2}}{25}=1 $$

Write an equation of the circle with the given center and radius. See Example 8. $$ (0,0) ; \sqrt{3} $$

Solve. The sum of the squares of two numbers is 130 . The difference of the squares of the two numbers is 32 . Find the two numbers.

Discuss how graphing a linear inequality such as \(x+y<9\) is similar to graphing a nonlinear inequality such as \(x^{2}+y^{2}<9\)

Solve. The sum of the squares of two numbers is \(20 .\) Their product is 8 . Find the two numbers.

Discuss how graphing a linear inequality such as \(x+y<9\) is different from graphing a nonlinear inequality such as \(x^{2}+y^{2}<9\)

Write an equation of the circle with the given center and radius. See Example 8. $$ (0,-6) ; \sqrt{2} $$

Identify whether each equation, when graphed, will be a parabola, circle,ellipse, or hyperbola. Sketch the graph of each equation. If a parabola, label the vertex. If a circle, label the center and note the radius. If an ellipse, label the center. If a hyperbola, label the \(x\) - or \(y\) -intercepts. $$ y^{2}=x^{2}+16 $$

Write an equation of the circle with the given center and radius. See Example 8. $$ (-5,4) ; 3 \sqrt{5} $$