Question

What is the equation of the circle in center - radius form: x² + y2 + 12x - 10y
- 7 = 0?

Answer 1

Answer:

Radius:  √ 61

Step-by-step explanation:

Complete the square for  x^ 2 + 12 x = ( x + 6 ) ^2 − 36

Substitute   ( x + 6 ) 2 − 36  for  x 2 + 12 x  in the equation  x 2 + y 2 + 12 x − 10 y = 0

= ( x + 6 ) 2 − 36 + y 2 − 10 y = 0

Move  − 36  to the right side of the equation by adding  36  to both sides

= ( x + 6 ) 2 + y 2 − 10 y = 0 + 36

Then you know the rest: radius will be √ 61

Answer 2

The center coordinate of the circle is (6,5) with a radius = 7.34

What is the equation of the circle?

The equation of the circle is: $(x-a)^{2} + (y-b)^{2} = r^{2} x^{2}$

Substituting the values in the equation:

$(x-a)^{2} + (y-b)^{2} = r^{2} x^{2} - 2ax + a^{2} + y^{2} - 2by +b^{2} - r^{2} = 0$

⇒  -2ax =  -12x

⇒  a = 6.

-2by = -10y

b= 5.

⇒ a² + b² - r² =  -7

⇒  6² + 5² + r² = -7

⇒ 36 + 25 + r² =  -7

⇒ r² = 54

⇒ r = 7.34

Center coordinate (6,5) with r = 7.34

Learn more about the equation of the circle here: brainly.com/question/1471134

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