What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5? f(x) = one eighth (x − 3)2 + 3 f(x) = −one eighth (x − 3)2 + 3 f(x) = one eighth (x − 3)2 − 3 f(x) = −one eighth (x − 3)2 − 3

Step-by-step explanation:

We want to find the equation of the parabola with a focus of and directrix .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

, where is the vertex of the parabola.

The axis of this parabola meets the directrix at .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

and .

The equation of the parabola now becomes,

.

Also is the distance between the vertex and the directrix.

This implies that .

Since the parabola turns downwards,

.

Our equation now becomes,

.

.

We make y the subject to get,

.

This is the same as

.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

1st part is 64,000,000

2nd part 500,000

step-by-step explanation: