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dem82 [27]
3 years ago
12

Find the center and radius of this circle. x2 + y2 − 40x − 24y + 15 = 0

Mathematics
1 answer:
Julli [10]3 years ago
5 0

ANSWER

Center: (20,12)

Radius:23

EXPLANATION

The given circle has equation:

{x}^{2}  +  {y}^{2}  - 40x - 24y + 15 = 0

We complete the square as follows:

{x}^{2}  - 40x +  {y}^{2}  - 24y =  - 15

{x}^{2}  - 40x +   {( - 20)}^{2} +  {y}^{2}  - 24y +  {( - 12)}^{2}  =  - 15+   {( - 20)}^{2}+  {( - 12)}^{2}

{(x - 20)}^{2} +  {(y - 12)}^{2}  =  - 15+   400+  144

{(x - 20)}^{2} +  {(y - 12)}^{2}  = 529

{(x - 20)}^{2} +  {(y - 12)}^{2}  =  {23}^{2}

Comparing this equation to:

{(x - h)}^{2} +  {(y - k)}^{2}  =  {r}^{2}

We have

(h,k)=(20,12)

representing the center and

r = 23

being the radius.

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\bf \begin{array}{ccccccccc}
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