Question

write the equation in the form ((x - h)^2 + (y - k)^2 = c). then, if the equation represents a circle, identify the center degenerate case, give the solution set.
(x^2 + y^2 - 10x + 2y + 35 = 0)
part: 0 / 2
part 1 of 2
the equation in standard form is (square).
the equation represents select (\boldsymbol{downarrow}).

Explanation:

Step1: Group x and y terms

$x^2 - 10x + y^2 + 2y = -35$

Step2: Complete the square for x

Take half of -10: $-5$, square it: $25$. Add to both sides.
$x^2 -10x +25 + y^2 +2y = -35 +25$

Step3: Complete the square for y

Take half of 2: $1$, square it: $1$. Add to both sides.
$(x^2 -10x +25) + (y^2 +2y +1) = -35 +25 +1$

Step4: Rewrite as perfect squares

$(x-5)^2 + (y+1)^2 = -9$

Answer:

The equation in standard form is $\boldsymbol{(x-5)^2 + (y+1)^2 = -9}$.
The equation represents a degenerate case, with no real solution set (since the right-hand side is negative, there are no real $(x,y)$ pairs that satisfy the equation).