Question

Determine the center and radius: x2 + y2 - 10x + 8y -8 = 0​

Answer 1

So our equation currently is ⇒ $x^2+y^2-10x+8y-8 = 0$

Let's first move all the constant to one side and group 'like variables' together:

      $(x^2-10x)+(y^2+8y) = 8$

Now lets complete the square of both equations

    $(x^2-10x+25)+(y^2+8y +16) = 8 + 25 + 16\\(x-5)^2+(y+4)^2 = 49\\(x-5)^2+(y+4)^2 = 7^2$

Now we know the circle's general equation format is:

   ⇒$(x-h)^2+(y-k)^2 = r^2$

• (h, k) ⇒ coordinate of the center of the circle
• r ⇒ length of radius of circle

Thus the radius of the circle is 7

Hope that helps!