Find the equation of a circle that has its center at (-4, 3) and has a radius of 5.

The resulting equation of the circle is x²+y²+8x-9y = 0

Step-by-step explanation:

The general form of equation of a circle is represented as:

(x-a)²+(y-b)² = r² with center (a,b) and radius r

Given the centre of (-4,3) and radius of 5

a = -4, b = 3, r = 5

Substituting this value into the general equation of a circle we have:

(x-(-4))²+(y-3)² = 5²

(x+4)²+(y-3)² = 5²

On expansion:

x²+8x+16+y²-9x+9 = 25

x²+y²+8x-9y+16+9-25 = 0

x²+y²+8x-9y = 0

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.