Question

The equation for the circle is:

x²+y²+14x+10y−7=0 .


What is the center of the circle?

Answer 1

centre = (- 7, - 5)

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Arrange the equation by placing the x and y terms together

x² + 14x + y² + 10y - 7 = 0 ( add 7 to both sides )

x² + 14x + y² + 10y = 7

Use the method of completing the square

add (half the coefficient of the x/y term)² to both sides

x² + 2(7)x + 7² + y² + 2(5)y + 5² = 7 + 7² + 5²

(x + 7)² + (y + 5)² = 7 + 49 + 25 = 81 ← in standard form

with (h, k) = (- 7, - 5) ← centre of circle

Answer 2

(-7,-5)

Explanation:

Converting the circle into the form (x-h)^2+(y-k)^2=r^2, we get

x^2+14x+49+y^2+10y+25=7+25+49

So we get

(X+7)^2+(y+5)^2=81

So the center of the circle is (-7,-5)