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 .

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for