Equations of Circles (x – a)2 + (y – b)2 = r2 (a, b) = center of the circle r = radius of the circle (x – 4)2 + (y + 3)2 = 36 What is the center and the radius of this circle? (4, -3) = center of the circle 6 = radius of the circle

Let’s Look at the Graph of (x – 4)2 + (y + 3)2 = 36 radius of the circle is 6 center of the circle is (4, -3)

Equations of an Ellipse Standard Form Intercept Form The center is the origin The center is the origin The center is the origin The center is the origin

Let’s Look at the Graph of 16x2 + 36y2 = 576 center of the ellipse is the origin x-intercepts are 6 y-intercepts are 4

Rewriting the Equation of an Ellipse Rewrite the following equation of an ellipse in intercept form. Rewrite the following equation of an ellipse in standard form. Just switch the coefficients of x and y. Since the equation must be equal to 1, divide by 400. Multiply by the common denominator. Simplify the fractions. Simplify the equation. I think I can do this without having to do too much work.

Graphing Circles and Ellipses Graph the following circle. Write the equation of the circle whose graph looks like this. 8 6 4 2 -2 -4 -6 -8 8 6 4 2 -2 -4 -6 -8 8 6 4 2 -2 -4 -6 -8 Graph the following ellipse. -8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8 Write the equations of the following two ellipses in both standard form and intercept form.

Equations of a Hyperbola xy = k As x increases, y decreases so that the product of x and y is always k xy = 8 As x increases, y decreases so that the product of x and y is always 8 A hyperbola is a function The coordinate axes are asymptotes of the graph When k > 0, the graph is in quadrant I and quadrant III When k < 0, the graph is in quadrant II and quadrant IV Each branch of the hyperbola is the reflection of the other in the origin

Let’s Look at the Graph of xy = 8 Since k > 0, the graph is in quadrant I and quadrant III The x and y axes are asymptotes of the graph

Let’s Look at the Graph of xy = -8 Since k < 0, the graph is in quadrant II and quadrant IV The x and y axes are asymptotes of the graph

Graphing Hyperbolas Solve the equation for y. Make a table of values. x y x y Since k is positive, the graph is in quadrants I and III Since k is negative, the graph is in quadrants II and IV

More Graphing Hyperbolas Solve the equation for y. Make a table of values. x y x y Since k is positive, the graph is in quadrants I and III Since k is positive, the graph is in quadrants I and III