Question

Reduce/Transform each equation to standard form and determine the center and radius. Show your complete solution.

a. x²+y²-6 x+8 y+20=0
b. x²+y²+24 y+95=0
c. 144 x²+14

Answer 1

To convert each equation to standard form, complete the square. The standard form of a circle equation is (x - h)² + (y - k)² = r².

Step-by-step explanation:

To transform each equation to standard form, we need to complete the square. The general standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

a. To convert x²+y²-6x+8y+20=0 to standard form:

1. Multiply the coefficients of x and y by 1/2: (x - 3)² + (y + 4)² = 9.
2. The center is (3, -4) and the radius is 3.

b. For x²+y²+24y+95=0:

1. Complete the square for y: x² + (y + 12)² = 104.
2. The center is (0, -12) and the radius is √104.

c. The equation 144x² +14 - 96x - 38y + 196 = 0 can't be converted to the standard circle form since it doesn't fit the general equation of a circle.