Question

the equation of a circle in expanded form is shown. what is the equation of the circle in standard form? use the drop - down menus to complete the equation. (x^{2}+y^{2}-8x + 4y-16 = 0). click the arrows to choose an answer from each menu. (( \text{choose... }x)^{2}+(\text{choose... })^{2}=\text{choose...})

Explanation:

Step1: Rearrange the terms

$x^{2}-8x + y^{2}-4y=16$

Step2: Complete the square for x - terms

$x^{2}-8x=(x - 4)^{2}-16$

Step3: Complete the square for y - terms

$y^{2}-4y=(y - 2)^{2}-4$

Step4: Substitute into the equation

$(x - 4)^{2}-16+(y - 2)^{2}-4=16$

Step5: Simplify the equation

$(x - 4)^{2}+(y - 2)^{2}=16 + 16+4$
$(x - 4)^{2}+(y - 2)^{2}=36$

Answer:

$(x - 4)^{2}+(y - 2)^{2}=36$