Question

write the equation in the form ((x - h)^2 + (y - k)^2 = c). then, if the equation represents a circle, identify the center and radii degenerate case, give the solution set.
(x^2 + y^2 - 10x + 4y - 20 = 0)
part: 0 / 2
part 1 of 2
the equation in standard form is (square).
the equation represents select.

Explanation:

Step1: Group x and y terms

$x^2 - 10x + y^2 + 4y = 20$

Step2: Complete the square for x

Take half of -10: $\frac{-10}{2}=-5$, square it: $(-5)^2=25$. Add to both sides.
$x^2 - 10x + 25 + y^2 + 4y = 20 + 25$

Step3: Complete the square for y

Take half of 4: $\frac{4}{2}=2$, square it: $2^2=4$. Add to both sides.
$x^2 - 10x + 25 + y^2 + 4y + 4 = 20 + 25 + 4$

Step4: Rewrite as perfect squares

$(x-5)^2 + (y+2)^2 = 49$

Answer:

The equation in standard form is $\boldsymbol{(x-5)^2 + (y+2)^2 = 49}$.
The equation represents a circle, with center $(5, -2)$ and radius $7$.