Question

Write the equation in standard form for the circle x2+y2–2y–43=0.

Answer 1

The general equation of a circle is:

(x-a)²+(y-b)²=r², where a and b are the coordinates of the center, and r is the radius.

Now: x²+y²-2y-43=0

x²+y²-2y+1-44=0

Sqrt(44)=6.63, so we get:

Answer: x²+(y-1)²=6.63²

Answer 2

x^2 + y(y - 2) = 43

Explanation:

Step 1: Add 43 to both sides

x^2 + y^2 - 2y - 43 + 43 = 0 + 43

x^2 + y^2 - 2y = 43

Step 2: Pull out the y from y^2 - 2y

x^2 + y^2 - 2y = 43

x^2 + y(y - 2) = 43

Answer: x^2 + y(y - 2) = 43