Which coordinate pair identifies the center of the circle represented by 4x2 + 4y2 - 16x - 24y + 36 = 0.

A) (2, 3)

B) (3, 2)

C) (0, 0)

D) (-3, 2)

Answer

Find out the which coordinate pair identifies the center of the circle represented by 4x² + 4y² - 16x - 24y + 36 = 0.

To prove

The general equation of the circle is

(x - h) ² + (y - k) ² = r²

Where h, k are the centre and r is the radius.

4x² + 4y² - 16x - 24y + 36 = 0

Divided both side by 4.

x² + y² - 4x - 6y + 9 = 0

Add and subtract 4 and 9

x² + y² - 4x - 6y + 4 - 4 + 9 - 9 + 9 = 0

x² + y² - 4x - 6y + 4 - 4 + 9 - 9 + 9 = 0

x² + 4 - 2 * 2 * x + y² + 9 - 2 * 3 * y = 9 + 4 - 9

using the formula (a + b) ² = a² + b² + 2ab

(x - 2) ² + (y - 3) ² = 2²

Compare this with the general equation of circle.

Thus

h = 2, k = 3

Option A is correct.