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Andrei [34K]
3 years ago
13

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9).

Mathematics
1 answer:
Svetllana [295]3 years ago
5 0
First we write standard form that includes both vertex and focus. The formula goes like this:

(x-h)^2 = 4*p*(y-k)

h and k are coordinates of vertex. since vertex is at beginning that means that h=k=0

p is focal lenght and in our case it is 9

expressing al of this we get:
x^2 = 4*9*y
x^2 = 36y
y = 1/36 * x^2
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Since the product of the slope is -1, hence the lines are perpendicular

<h3>Parallel and Perpendicular lines</h3>

Two lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1

Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;

Slope = 4-6/6-0
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Learn more on parallel and perpendicular lines here: brainly.com/question/25429151

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When the positive integer n is divided by 7, the remainder is 2. What is the remainder when 5n is divided by 7?
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Therefore the reminder is 3 when 5n is divided by 7.

Step-by-step explanation:

we know that

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multiplying by 5 both sides

5n = 5 Q(n) ×7 + 2×5

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