write the equation x^2-18y+y^2+14x+10=0. what is the center and radius of this circle

Question

hero · Answer

$x^2 - 18y + y^2 + 14x + 10 = 0$

Place all non-$x$ terms on the right side

$x^2 + 14x = 18y - y^2 - 10$

Complete the square on $x^2 + 14x$ by adding $7^2$ to both sides:

$x^2 + 14x + 49 = 18y - y^2 - 10 + 49$

$(x+7)^2 = 18y - y^2 - 39$

hero · Answer

Correction:

$(x + 7)^2 = 18y - y^2 + 39$

hero · Answer

Now Isolate $y^2 - 18y$

$y^2 - 18y = -(x + 7)^2 + 39$

Now complete the square on $y^2 - 18y$ by adding 81 to both sides:

$y^2 - 18y + 81 = -(x + 7)^2 + 39 + 81$
$(x + 7)^2 + (y - 9)^2 = 120$

hero · Answer

The center of the circle would be (-7, 9)

The radius of the circle would be $\sqrt{120}$