Question

a. type the equation in center - radius form.
$(x + 4)^{2}+(y - 3)^{2}=16$
(simplify your answer.)
b. type the equation in general form.
(simplify your answer.)

Explanation:

Step1: Expand \((x + 4)^2\)

Using the formula \((a + b)^2=a^{2}+2ab + b^{2}\), we have \((x + 4)^2=x^{2}+8x + 16\)

Step2: Expand \((y - 3)^2\)

Using the formula \((a - b)^2=a^{2}-2ab + b^{2}\), we have \((y - 3)^2=y^{2}-6y + 9\)

Step3: Substitute into the original equation

The original equation \((x + 4)^2+(y - 3)^2 = 16\) becomes \(x^{2}+8x + 16+y^{2}-6y + 9=16\)

Step4: Simplify the equation

Combine like - terms: \(x^{2}+y^{2}+8x-6y+16 + 9-16=0\), which simplifies to \(x^{2}+y^{2}+8x-6y + 9=0\)

Answer:

\(x^{2}+y^{2}+8x-6y + 9=0\)