Question

Please help!!!!!
The equation of a circle is x² + y² – 8x + 10y + 37 = 0. What is the center and the radius of the circle? Show all your work.

Answer 1

Let's take this problem step-by-step:

 

Let's convert the equation back into the standard form:

     ⇒ standard form: (x-h)² +(y-k)² = r²

• (h, k): center's coordinate
• r: radius

       $x^2+y^2-8x+10y + 37 = 0\\\rm \hookrightarrow x^2 - 8x + y^2+10y = -37\\\rm \hookrightarrow (x^2 - 8x) + (y^2 + 10y) = -37\\\rm \hookrightarrow (x^2-8x+16) + (y^2+10y+25) = -37 + 16 +25\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 4\\\rm \hookrightarrow (x-4)^2 + (y+5)^2 = 2^2$

Based on the equation found

  ⇒ center: (4, -5)

   ⇒ radius: 2

Answer:

• center: (4, -5)

• radius: 2

Hope that helps!

#LearnwithBrainly