How do you convert 3x^+2x+3y^-7y-10=0 from standard form to center radius form?

Question

I need step by step instructions

Answer 1

Do you mean this equation?

3x² + 2x + 3y² - 7y - 10 = 0

 

If so, then this is how you would rearrange it to find the centre and the radius.

 

3(x² +(2/3)x) + 3(y² - (7/3)y) - 10 = 0

Divide through by 3 :
 

(x² + (2/3)x) + (y² - (7/3)y) - (10/3) = 0

Now you can complete the square:

 

(x + (2/6))² - (2/6)² + (y - (7/6))² - (7/6)² - (10/3) = 0

(x + 1/3)² + (y - 7/6)² = 49/36 + 4/36 + 10/3

(x + 1/3)² + (y - 7/6)² = (1/36)(49 + 4 + 10*12)

(x + 1/3)² + (y - 7/6)² = 173/36

 

This means that the centre of the circle is (-1/3, 7/6) and the radius is 173/36 .