Question

The general form of a circle is given as x^2 +y^2 +4x - 12y + 4 = 0.

Answer 1

Part 1) The general form of a circle is given as x²+y² +4x - 12y + 4 = 0.

(a)What are the coordinates of the center of the circle?
(b)What is the length of the radius of the circle?

x²+y² +4x - 12y + 4 = 0

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

(x²+4x)+(y²- 12y)=-4

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

(x²+4x+4)+(y²- 12y+36)=-4+4+36

Rewrite as perfect squares

(x+2)²+(y-6)²=36--------> (x+2)²+(y-6)²=6²
center (-2,6)
radius 6

the answer Part a) is 
the center is the point (-2,6)

the answer Part b) is
the radius is 6

Part 2) A 10-foot ladder placed on level ground leans against the side of a house. The ladder reaches a point that is 9.2 feet up on the side of the house.
(a)What is the measure of the angle formed by the ladder and the level ground? Round your answer to the nearest degree.

see the picture attached N 1 to better understand the problem

we know that
sin ∅=opposite side angle ∅/hypotenuse
opposite side angle ∅=9.2 ft
hypotenuse=10 ft
so
sin ∅=9.2/10-----> 0.92
∅=arc sin (0.92)------> ∅=66.93°-----> ∅=67°

the answer Part a) is 
67°

Part b) The same 10-foot long ladder is placed against the building according to OSHA’s safety standard. 
What is the distance between the foot of the ladder and the foot of the building? Round your answer to the nearest tenth.

see the picture attached N 2 to better understand the problem

cos 75=adjacent side angle 75/hypotenuse
adjacent side angle 75=AC
hypotenuse=10 ft
so
cos 75=AC/10---------> AC=10*cos 75----> AC=2.59 ft----> AC=2.6 ft

the answer Part b) is
Distance between the foot of the ladder and the foot of the building is 2.6 ft