Question

find the center and radius of the circle having the given equation. $x^{2}+y^{2}-2x - 4y-20 = 0$ radius: center: ( ) question help: video ebook written example

Explanation:

Step1: Complete the square for x - terms

Group the x - terms and y - terms: $(x^{2}-2x)+(y^{2}-4y)=20$.
For the x - terms, $x^{2}-2x=(x - 1)^{2}-1$.

Step2: Complete the square for y - terms

For the y - terms, $y^{2}-4y=(y - 2)^{2}-4$.
So, $(x - 1)^{2}-1+(y - 2)^{2}-4=20$.

Step3: Rewrite the equation in standard form

$(x - 1)^{2}+(y - 2)^{2}=20 + 1+4$.
$(x - 1)^{2}+(y - 2)^{2}=25$.

Answer:

Radius: $5$
Center: $(1,2)$