Question

The general form of the equation of a circle is x²+y²+8x+22y+37=0 The equation of this circle in standard form is (x-4)² +(y-11)² =100 The center of the circle is at the point(4,11)

a. True
b. False

Answer 1

The equation of the given circle is x²+y²+8x+22y+37 = 0. To write this equation in standard form, we need to complete the square for both x and y terms. The standard form of the equation of the circle is (x - 4)² + (y - 11)² = 100. The center of the circle is at the point (4, 11).

Step-by-step explanation:

The equation of the given circle is x²+y²+8x+22y+37 = 0. To write this equation in standard form, we need to complete the square for both x and y terms.

Step 1: Complete the square for x term, which gives (x + 4)² + y² + 22y + 37 = 16.

Step 2: Complete the square for y term, which gives (x + 4)² + (y + 11)² = 100.

The standard form of the equation of the circle is (x - 4)² + (y - 11)² = 100. The center of the circle is at the point (4, 11). Therefore, the statement (a) True is correct.