# College Algebra

posted by .

Find the center (h,k) and the radius (r) of the circle with the given equations:

1. 2(x-2)^2+2(y+5)^2=28

2. 4x^2+4y^2-12x+16y-5=0

• College Algebra -

#1 is easy. just read them out of the equation. Divide by 2 to make it easier.

#2: (4x^2 - 12x) + (4y^2 + 16y) = 5
or
4(x^2 - 3x) + 4(y^2 + 4y) = 5

(x^2 - 3x) + (y^2 - 4y) = 5/4

Now, you need to make the parenthesized terms perfect squares by adding extra constants on both sides of the equation:

(x^2 - 3x + 9/4) + (y^2 - 4y + 4) = 5/4 + 9/4 + 4

(x - 3/2)^2 + (y - 2)^2 = 15/2

now you can read off h,k r^2 from that

• College Algebra -

8,9), x + 2y = 7 please solve this for me

## Similar Questions

1. ### college algebra

Find the center and radius of the circle (x+3)^2+(y-5)^2=13 I think the center is (-3,5) Radius is (13) but I don't know how to show the work for it.

3. ### geometry

Find the coordinates of the center and the radius of a circle with and equation of: a. x^2 + 2root7x +7 + (Y-root 11)^2 =11 b. x^2 -12x + 84 =-y^2 + 16y
4. ### College Algebra

using the knowledge of systems of equations, and that the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius. Find the equation of a circle that contains the following points: (6,2), (4,6), …
5. ### College Algebra

using the knowledge of systems of equations, and that the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius. Find the equation of a circle that contains the following points: (6,2), (4,6), …
6. ### NEED MAJOR HELP! *QUADRATIC EQUATIONS*

Write the equation for the circle with center at (- 8, - 6) and radius of 10. (x+8)² + (y + 6)² = 10 (x+8)² + (y + 6)² = 100 (x-8)² + (y - 6)² = 100 Find the standard equation for the circle with center on the positive x-axis …
7. ### College Algebra

Write the equation of a circle in standard Find the center, radius intercepts and graph the circle. .........x^2+y^2-12x-4y+36=0
8. ### Algebra

Find the equation of the circle having the given center and radius. center (-5,1), radius 6 squared.
9. ### college pre-calculus

4x^2+4y^2-16x-24y+51=0 is the equation of a circle. where is the center of the circle and what is it's radius?
10. ### Geometry

Write the General form equations for the following circles: 1. A circle with center (1, -6) and radius 4 2. A circle with center (6, 8) and radius 10 3. A circle with center (0, 3) and radius 2√3 4. A circle with center (-0.5, 5.5 …

More Similar Questions