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 .

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square