Question

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.

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

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