Question

A certain circle can be represented by the following equation x^2+y^2+18x+14y+105=0 What is the center and radius of the circle?

Answer 1

Answer:

• center: (-9, -7)
• radius: 5

Step-by-step explanation:

A graphing calculator can be helpful for questions of this nature. The attached shows the center is (-9, -7) and the radius is 5.

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You can separate the x- and y- terms and complete the square for each.

  (x^2 +18x) +(y^2 +14y) = -105

Do that by adding the square of half the linear term.

  (x^2 +18x +9^2) +(y^2 +14x +7^2) = -105 +81 +49

  (x +9)^2 +(y +7)^2 = 25

Compared to the standard form equation ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . . center (h, k), radius r

We see that the given circle has a center of (-9, -7) and a radius of 5.