Precalculus!! Please help!!!?

Question

1. What are the focus and the directrix of the graph of x = 1/24 y^2
A. focus (0, –6), directrix x = 6
B. focus (6, 0), directrix x = –6
C. focus (0, 6), directrix y = –6
D. focus (–6, 0), directrix y = 6

2. Write an equation of a circle with the given center and radius. 

center (–7, –6) and radius 2 (1 point)

A. (x + 7)2 + (y + 6)2 = 4
B. (x – 7)2 + (y – 6)2 = 2
C. (x + 7)2 + (y + 6)2 = 2
D. (x – 7)2 + (y – 6)2 = 4

3. What is the center and radius of the circle with the given equation? 

(x – 1)2 + (y + 1)2 = 4 (1 point)

A.center (–1, 1); radius 4
B. center (1, –1); radius 4
C. center (–1, 1); radius 2
D. center (1, –1); radius 2

PLEASE HELP!

Answer 1

2). The center if (- 7, - 6) and the radius is 2

The standard form for the equation of a circle in a Cartesian coordinate system is (x - h)² + (y - k)² = r²,

Substitute (h, k) = (- 7, - 6) and r = 2 in the equation.

[x - (-7)]² + [y - (-6)]² = 2²

[x + 7]² + [y + 6]² = 4

Option A is right choice.

Answer 2

3). (x – 1)² + (y + 1)² = 4

Rewrite the equation (x –1))² + (y –(–1))² = 2²

Compare equation with standard from (x - h)² + (y - k)² = r²

Where h = 1, k = –1 and r = 2.

Therefore center if (h, k) = (1, –1) and the radius is r = 2.

Option D is right choice.

Answer 3

1) Parabola equation

In this case the y part is squred, So this is horizontal parabola.

Compare it to standard form of parabola

Where , vertex is , focus and Directrix is

Compare it to

P  > 0 the parabola opens right.

vertex is

In this case vertex is (0, 0).

Directrix is

Directrix x = 0 - 6

x = - 6

And focus is at

Focus = (0 + 6, 0) = (6, 0)

Focus is (6, 0) and directrix x  = -6.

Option B is correct choice.