A circle has the equation x2+y2-14x-18y+105=0.

What is the equation of the circle in standard form, the location of its center, and the length of its radius?

The equation of the circle is (x+7) 2 + (y+9) 2=25; the center is at (-7,-9), and the radius is 5 units.

The equation of the circle is (x+7) 2 + (y+9) 2=89; the center is at (-7,-9), and the radius is 89--√ units.

The equation of the circle is (x-7) 2 + (y-9) 2=415; the center is at (7,9), and the radius is 415---√ units.

The equation of the circle is (x-7) 2 + (y-9) 2=25; the center is at (7,9), and the radius is 5 units.

Question

Mathematics

Mia Waters

20 October, 15:22

A circle has the equation x2+y2-14x-18y+105=0.

What is the equation of the circle in standard form, the location of its center, and the length of its radius?

The equation of the circle is (x+7) 2 + (y+9) 2=25; the center is at (-7,-9), and the radius is 5 units.

The equation of the circle is (x+7) 2 + (y+9) 2=89; the center is at (-7,-9), and the radius is 89--√ units.

The equation of the circle is (x-7) 2 + (y-9) 2=415; the center is at (7,9), and the radius is 415---√ units.

The equation of the circle is (x-7) 2 + (y-9) 2=25; the center is at (7,9), and the radius is 5 units.

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Answers (1)

Know the Answer?

Mariana Newton · Answer 1

The answer to your question is the last option

Equation in standard form = (x - 7) ² + (y - 9) ² = 5²

Center = (7, 9)

Radius = 5

Step-by-step explanation:

Equation

x² + y² - 14x - 18y + 105 = 0

- Grouping property

(x² - 14x) + (y² - 18y) = - 105

- Complete perfect square trinomials

(x² - 14x + 7²) + (y² - 18y + 9²) = - 105 + 49 + 81

- Factor

(x - 7) ² + (y - 9) ² = 25

or (x - 7) ² + (y - 9) ² = 5²

Center = (7, 9)

Radius = 5