Question

Rewrite the equation of a circle given below in standard formx² - 18x+ y² + 8y + 28 = 0

Answer 1

B. (x-9)²+(y+4)²=69

Step-by-step explanation:

The standard form of the equation of a circle is given as:

`(x-h)^2+(y-k)^2=r^2`

Given the circle:

`x^2-18x+y^2+8y+28=0`

Complete the square in each variable to obtain the standard form.

First, take the constant to the right-hand side of the equation.

`x^2-18x+y^2+8y=-28`

Next, we divide the coefficient of x (same for y) by 2, square it and add it to both sides.

`x^2-18x+(-9)^2+y^2+8y+(4^2)=-28+(-9)^2+(4^2)`

Write the left-hand side as a square while the right-hand side is simplified.

`(x-9)^2+(y+4)^2=69`

The correct choice is B.