Question

Can someone please help me with these geometry questions I will mark brainliest

Answer 1

Answer:

28) E

31) D

32) B

26) E

Step-by-step explanation:

Question 28

Equation of a circle: (x - a)² + (y - b)² = r²

where (a, b) is the center of the circle, and r is the radius

Given:

• center = (-5, 5)
• radius = 3

⇒ (x + 5)² + (y - 5)² = 9

Question 31

Vertical Parabola Equation: $y=\dfrac{1}{4p}(x-h)^2+k$  

where

• vertex:  (h, k)
• focus:  (h, k + p)
• directrix:  y = k - p

The vertex of the parabola is at equal distance between focus and the directrix.

If the focus is (9, 27) and the directrix is at y = 11,

then the y-coordinate of the vertex will be:  (27 - 11)/2 + 11 = 19

So the vertex is (9, 19)

Also, y-coordinate of focus:  19 + p = 27  ⇒ p = 8

$\implies f(x)=\frac{1}{32}(x-9)^2+19$

Question 32

Horizontal Parabola Equation: $x=\dfrac{1}{4p}(y-k)^2+h$  

where

• vertex:  (h, k)
• focus:  (h + p, k)
• directrix:  x = h - p

The vertex of the parabola is at equal distance between focus and the directrix.

If the focus is (-1, 15) and the directrix is at x = -4,

then the x-coordinate of the vertex will be: (-1 + 4)/2 = -2.5

So the vertex is (-2.5, 15)

Also,  -2.5 - p = -4  ⇒  p = 1.5

$\implies x=\dfrac{1}{6}(y-15)^2-\dfrac52$

Question 26

$(x - 3)^2+(y+4)^2=6^2$

Domain:  3 - 6 ≤ x ≤ 3 + 6  ⇒  -3 ≤ x ≤ 9

Range:  -4 - 6 ≤ y ≤ -4 + 6  ⇒  -10 ≤ y ≤ 2

Therefore, the only point that satisfies the above domain and range is

(-3, -4)