SOLUTION: 4.Find the center and radius of the circle whose equation is x2 + 10x + y2= 75. a. C(–10, 0), r = 100 b. C(–10, 0), r = 10 c. C(–5, 0), r = 100 d. C(–5, 0), r = 10

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Question 319357: 4.Find the center and radius of the circle whose equation is x2 + 10x + y2= 75.
a. C(–10, 0), r = 100
b. C(–10, 0), r = 10
c. C(–5, 0), r = 100
d. C(–5, 0), r = 10

5. Find the foci of the ellipse with the following equation.
(x - 1)^2/9 + (y+2)^2/25 =1

A. F1(5, –2), F2(–3, –2)
b. F1(1, 2), F2(1, –6)
c. F1(4, –2), F2(–2, –2)
d. F1(1, 1), F2(1, –5)
6. Find the slopes of the asymptotes of a hyperbola with the following equation.
y^2/81 - x^2/64 = 1

a. 8/9
b. 9/8
c. 8/9, –8/9
d. 9/8, –9/8
7.Identify the type of equation presented in x2 + y2 – 4x + 12y – 6 = 0.
a. parabola
b. circle
c. ellipse
d. hyperbola
8. Solve the following system of equations.
x2 + y2 = 64
x2 + 64y2 = 64
a. (8, 0), (–8, 0)
b. (0, 8), (0, –8)
c. (8, 0)
d. (0, –8)
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Sorry, only one question per post.



Complete the square on the terms.

The lead coefficient on the terms is 1, so simply divide the 1st degree term coefficient by 2 and square the result. Add that result to both sides of the equation. Since there is no 1st degree term, there is no need to complete the square on



Factor the perfect square in in the LHS.



Then use the fact that the equation of a circle with center at and radius is:



And the facts that and

To determine that the circle's center is at and that the radius is

John
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