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TEA [102]
2 years ago
10

What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?

Mathematics
1 answer:
frosja888 [35]2 years ago
3 0

ANSWER

The radius is 4

EXPLANATION

The given equation is:

{x}^{2}  +  {y}^{2}  - 10y + 6x + 18 = 0

We complete the square to get the expression in standard form:

{x}^{2}  + 6x +  {y}^{2}  - 10y  + 18 = 0

{x}^{2}  + 6x +  9 + {y}^{2}  - 10y  + 25  =  - 18 + 9 + 25

We factor using perfect squares to get:

{(x + 3)}^{2}  +  {(y - 5)}^{2} =  16

This implies that,

{(x + 3)}^{2}  +  {(y - 5)}^{2} =   {4}^{2}

Comparing to

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

The radius is r=4

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