Question

The equation of a circle is ​x2+4x+y2−10y+13=0​ .

What is the equation of the circle in standard form?

(x+4)2+(y−25)2=25

(x+4)2+(y−25)2=16

(x+2)2+(y−5)2=16

(x+2)2+(y−5)2=25

Answer 1

x^2+4x+4+y^2-10y+25=-13+25+4

(x+2)^2 + (y-5)^2= 16
Third option

Answer 2

`(x+2)^2+(y-5)^2=16`

Explanation:

Given :
`x^2+4x+y^2-10y+13=0`

To Find: What is the equation of the circle in standard form?

Solution:

`x^2+4x+y^2-10y+13=0`

`x^2+4x+2^2-2^2+y^2-10y+5^2-5^2+13=0`

`(x+2)^2-4+(y-5)^2-25+13=0`

`(x+2)^2+(y-5)^2-29+13=0`

`(x+2)^2+(y-5)^2-16=0`

`(x+2)^2+(y-5)^2=16`

Hence the equation of the circle in standard form is
`(x+2)^2+(y-5)^2=16`

So, Option C is correct.