Question

a. type the equation in center - radius form.
$(x - 5)^{2}+(y - 2)^{2}=25$
(simplify your answer.)
b. type the equation in general form.
(simplify your answer.)

Explanation:

Step1: Expand \((x - 5)^2\)

Using the formula \((a - b)^2=a^{2}-2ab + b^{2}\), we have \((x - 5)^2=x^{2}-10x + 25\)

Step2: Expand \((y - 2)^2\)

Using the formula \((a - b)^2=a^{2}-2ab + b^{2}\), we have \((y - 2)^2=y^{2}-4y + 4\)

Step3: Substitute into the original equation

The original equation \((x - 5)^2+(y - 2)^2 = 25\) becomes \(x^{2}-10x + 25+y^{2}-4y + 4=25\)

Step4: Simplify the equation

Combine like - terms: \(x^{2}+y^{2}-10x-4y+29 = 25\)
Then subtract 25 from both sides: \(x^{2}+y^{2}-10x-4y+4 = 0\)

Answer:

\(x^{2}+y^{2}-10x - 4y+4 = 0\)