Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. which statements are true? check all that apply.
a. to begin converting the equation to standard form, subtract 36 from both sides.
b. to complete the square for the x terms, add 4 to both sides.
c. the center of the circle is at (–2, 3).
d. the center of the circle is at (4, –6).
e. the radius of the circle is 6 units.
f. the radius of the circle is 49 units.

we have

we know that

the equation of a circle in standard form is equal to

where

(h,k) is the center of the circle

r is the radius of the circle

Convert the equation to standard form

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

so

Adds both sides

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

Rewrite as perfect squares

the center of the circle is the point

the radius of the circle is units

Let's verify each of the statements

Statements

case A) To begin converting the equation to standard form, subtract from both sides

The statement is false

because, To begin converting the equation to standard form, adds from both sides

case B) To complete the square for the x terms, add to both sides

The statement is true

see the procedure

case C) The center of the circle is at

The statement is true

see the procedure

case D) The center of the circle is at

The statement is false

the center of the circle is the point (see the procedure)

case E) The radius of the circle is units

The statement is false

the radius of the circle is units (see the procedure)

case F) The radius of the circle is units

The statement is false

the radius of the circle is units (see the procedure)

therefore

the answer is

B. To complete the square for the x terms, add to both sides

C. The center of the circle is at

b is the answer that makes most sense

step-by-step explanation:

f(x) = y

f(-3) = -5

step-by-step explanation: