3.2 "Graphs of Equations"
Sketch the graph of the equation, & label x and y­intercepts.
(ex) y = ­2x ­ 3 y
x
(ex) y = ­x2 + 2
x
y
(ex) x = 2y2 ­ 4
x
y
(ex) y = ­x3 + 1
x
y
(ex)
x
y
(ex)
x
y
Sketch the graph of the circle.
(ex) x2 + y2 = 7
(ex) (x ­ 4)2 + (y + 2)2 = 4
Sketch the graph of the semicircle.
(ex) Using the distance formula:
P(x,y)
r
C(h,k)
Standard Equation of a circle:
(x ­ h)2 + (y ­ k)2 = r2
Find an equation of the circle that satisfies the given conditions:
(ex) Center C(­4, 1), radius 3
Standard Equation of a circle:
(x ­ h)2 + (y ­ k)2 = r2
(ex) Center at origin, passing through P(4, ­7)
(ex) Center C(4, ­1), tangent to the x­axis.
(ex) Tangent to both axes, center in 4th quadrant, radius 3
(ex) Endpoints of a diameter A(­5, 2) and B(3, 6)
Find the center and radius of a circle.
(ex) x2 + y2 + 8x ­ 10y + 37 = 0
(ex) x2 + y2 ­ 10x + 18 = 0
(ex) x2 + y2 ­ 6x + 4y + 13 = 0
Find equations for the upper half, lower half, right half, & left half of the circle. "semi­circles"
(ex) (x ­ 3)2 + (y ­ 5)2 = 4
(ex) Determine whether the point P is inside, outside, or on the circle with center C and radius r.
P(­2, 5), C(3, 7), r = 6
(ex) Find the (a) x­intercepts and (b) y­intercepts of the given circle.
x2 + y2 ­ 10x + 4y + 13 = 0
(ex) Estimate the coordinates of the intersections of these equations.
(ex) A circle C1 of radius 5 has its center at the origin. Outside this circle is a first­quadrant circle C2 of radius 2 that is tangent to C1. The y­coordinate of
the center of C2 is 3. Find the x­coordinate of the center of C2.