Answer:

Center = (2, 3) radius =

Explanation:
When both the x² and y² values are equal and positive, the shape is a circle. Complete the square to put the equation in format:
(x-h)² + (y-k)² = r² where
- (h, k) is the vertex
- r is the radius
1) Group the x's and y's together and move the number to the right side
4x² - 16x + 4y² - 24y = -51
2) Factor out the 4 from the x² and y²
4(x² - 4x ) + 4(y² - 6y ) = -51
3) Complete the square (divide the x and y value by 2 and square it)
![4[x^2-4x+\bigg((-4)/(2)\bigg)^2]+4[y^2-6y+\bigg((-6)/(2)\bigg)^2]=-51+4\bigg((-4)/(2)\bigg)^2+4\bigg((-6)/(2)\bigg)^2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8g8atfuz7qst3c51r9y2yh15qcy694u7fq.png)
= 4(x - 2)² + 4(y - 3)² = -51 + 4(-2)² + 4(-3)²
= 4(x - 2)² + 4(y - 3)² = -51 + 4(4) + 4(9)
= 4(x - 2)² + 4(y - 3)² = -51 + 16 + 36
= 4(x - 2)² + 4(y - 3)² = 1
4) Divide both sides by 4

- (h, k) = (2, 3)
