Test B review, no calculators please help

Question

Answer 1

20).

The standard form of the circle equation is ( x - h )² + ( y - k )² = r², where, (h, k) is the center of the circle, and r is the radius.

The circle equation is x² + 12x + y² - 8y = - 43.

Write the equation in standard form of a circle.

To change the expression into a perfect square  add (half the x coefficient)² and add (half the y coefficient)²to each side of the expression.

Here, x coefficient = 12, so, (half the x coefficient)² = (12/2)²= 36.

Here, y coefficient = - 8, so, (half the y coefficient)² = (- 8/2)²= 16.

Add 36 and 16 to each side.

x² + 12x + 36 + y² - 8y + 16 = - 43 + 36 + 16

(x + 6)² + (y - 4)² = 9

(x - (- 6))² + (y - 4)² = 3²

Compare the equation with standard form of a circle equation.

The center (h, k) is (- 6, 4), and

The radius (r) is 3 units.

Solution : Option (e) is the correct choice.