MATH SOLVE

2 months ago

Q:
# Identify the center and radius from the equation of the circle given below. x^2+y^2+121-20y=-10x

Accepted Solution

A:

Answer: Center: (-5,10) Radius: 2Step-by-step explanation: The equation of the circle in center-radius form is: [tex](x-h)^2+(y-k)^2=r^2[/tex] Where the point (h,k) is the center of the circle and "r" is the radius. Subtract 121 from both sides of the equation: [tex]x^2+y^2+121-20y-121=-10x-121\\x^2+y^2-20y=-10x-121[/tex] Add 10x to both sides: [tex]x^2+y^2-20y+10x=-10x-121+10x\\x^2+y^2-20y+10x=-121[/tex] Make two groups for variable "x" and variable "y": [tex](x^2+10x)+(y^2-20y)=-121[/tex] Complete the square: Add [tex](\frac{10}{2})^2=5^2[/tex] inside the parentheses of "x". Add [tex](\frac{20}{2})^2=10^2[/tex] inside the parentheses of "y". Add [tex]5^2[/tex] and [tex]10^2[/tex] to the right side of the equation. Then: [tex](x^2+10x+5^2)+(y^2-20y+10^2)=-121+5^2+10^2\\(x^2+10x+5^2)+(y^2-20y+10^2)=4[/tex] Rewriting, you get that the equation of the circle in center-radius form is: [tex](x+5)^2+(y-10)^2=2^2[/tex] You can observe that the radius of the circle is: [tex]r=2[/tex] And the center is: [tex](h,k)=(-5,10)[/tex]