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Verizon [17]
2 years ago
12

Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?

Mathematics
1 answer:
kramer2 years ago
3 0

Answer:

y = 1/12 (x − 5)²

Step-by-step explanation:

We can solve this graphically without doing calculations.

The y component of the focus is y = 3.  Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient.  That narrows the possible answers to A and C.

The x component of the focus is x = 5.  Since this is above the vertex, we know the x component of the vertex is also x = 5.

So the answer is A. y = 1/12 (x−5)².

But let's say this wasn't a multiple choice question and we needed to do calculations.  The equation of a parabola is:

y = 1/(4p) (x − h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

The vertex is halfway between the focus and the directrix.  So p is half the difference of the y components:

p = (3 − (-3)) / 2

p = 3

k, the y component of the vertex, is the average:

k = (3 + (-3)) / 2

k = 0

And h, the x component of the vertex, is the same as the focus:

h = 5

So:

y = 1/(4×3) (x − 5)² + 0

y = 1/12 (x − 5)²

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An angle measures 68° more than the measure of a complementary angle. What is the measure of each angle?
kifflom [539]

Answer:

11° and 79°

Step-by-step explanation:

Complementary angles sum to 90°

let x be one angle then the other angle = x + 68 , hence

x + x + 68 = 90

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I forgot how to do this. I will give brainliest!
Hitman42 [59]

Answer:

A = 2, B = 3 and C = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y = 2 ( subtract 2x from both sides )

3y = - 2x + 2 ( divide all terms by 3 )

y = - \frac{2}{3} x + \frac{2}{3} ← in slope- intercept form

with slope m = - \frac{2}{3}

Parallel lines have equal slopes, thus

y = - \frac{2}{3} x + c ← is the partial equation

To find c substitute (2, 0) into the partial equation

0 = - \frac{4}{3} + c ⇒ c = \frac{4}{3}

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Multiply through by 3

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with A = 2, B = 3 and C = 4

4 0
2 years ago
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