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marishachu [46]
2 years ago
14

A parabola can be drawn given a focus of (5, -3) and a directrix of y=1. Write the equation of the parabola in any form.

Mathematics
1 answer:
Anna71 [15]2 years ago
6 0

Answer:

(x²-10x+33)/(-8) = y

Step-by-step explanation:

The distance between any point on a parabola from both its focus and directrix are the same.

Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,

\sqrt{(x-5)^2+(y-(-3))^2}is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.

Equating the two equations given, we have

\sqrt{(x-5)^2+(y-(-3))^2} = |y-1|

square both sides to get

(x-5)²+(y+3)²=(y-1)²

expand the y components

(x-5)² + y²+6y+9 = y²-2y+1

subtract y²+6y+9 from both sides

(x-5)² = -8y - 8

expand the x components

x²-10x+25 = -8y - 8

add 8 to both sides to isolate the -8y

x²-10x+33 = -8y

divide both sides by -8 to isolate y

(x²-10x+33)/(-8) = y

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Answer:

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Step-by-step explanation:

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Combine like terms

<em>q</em> = 12<em>x</em>

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(-1,2) (1,8)<br><br> Find the slope
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2 years ago
Which equation is modeled by the graph? Using the equation, about how many more cars are in the deck at 9:00 a.m. than at 8:30 a
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6 0
3 years ago
Read 2 more answers
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Answer:

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While traveling to the office, dolly drives her car at a speed of 60 kmph and then suddenly the car stopped on half of her dista
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The average speed of Dolly is 33.33kmph.

Average Speed:

The average speed is defined as the total distance travelled by the object in a particular interval of time. It can be calculated by dividing the total distance travelled by the total time taken.

So, Average Speed = total distance / total time

Here,

Let the total distance is 100 km.

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To know more about Average speed here

brainly.com/question/12322912

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