Name ___Answers______      Precalculus Exploration 4 Quiz    Date ____________                   

Note that you must show all work on each problem to get full credit.

1.  Write an equation of the circle that is tangent to the y-axis and whose center is (2, 3).

(x-2)^2+(y-3)^2 = 4

[Maple Plot]

2.  Rewrite the equation of the circle below in standard form and find its center and radius. Also, accurately sketch the circle.

2*x^2-4*x+2*y^2-y = -1/8

2*(x-1)^2-17/8+2*(y-1/4)^2 = -1/8

2*(x-1)^2+2*(y-1/4)^2 = 2

(x-1)^2+(y-1/4)^2 = 1

[Maple Plot]

3.  Find any points of intersection of the following line and circle, and accurately sketch the two figures.

y = -1/2*x-1/2, `  `*(x+1)^2+(y+2)^2 = 25

[Maple Plot]

`Substitute: `*y = -1/2*x-1/2, ` into `*((x+1)^2+(y+2)^2) = 25

(x+1)^2+(-1/2*x+3/2)^2 = 25

5/4*x^2+1/2*x+13/4 = 25

5/4*x^2+1/2*x-87/4 = 0

5*x^2+2*x-87 = 0

x = -1/5-2/5*109^(1/2), -1/5+2/5*109^(1/2), ` `*y = -2/5+1/5*109^(1/2), -2/5-1/5*109^(1/2)

`Intersection Points: `*[x[1], y[1]] = [-4.36, 1.68], [x[2], y[2]] = [3.96, -2.48]