Mrs. culland is finding the center of a circle whose equation
is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. her
work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (x2 + 4y + 4) = 3 + 9 + 4

The center of the circle is (-3,-2)

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

where

(h,k) is the center

r is the radius

In this problem we have

Completing the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

therefore

The center of the circle is (-3,-2)

c is the final answer! : )

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.