Convert this Polar Equation to a Rectangular Equation
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Convert this Polar Equation to a Rectangular Equation

[From: ] [author: ] [Date: 11-05-31] [Hit: ]
...y^2 = 25-10xthis is the answer.......
The polar equation is:

r = 5 / (1+cosθ)

The options are:

A.
x^2 = 25y - 10

B.
x^2 = 10 - 25y

C.
y^2 = 25x - 10

D.
y^2 = 10 - 25x

Or something very similar to those options. (I'm doing this from memory.) I'm really stuck on how to solve this. Can anyone show me how to arrive at an answer, please?

Thanks.

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well what i did was i multiplied both sides by (1+cosθ), then you have r+rcosθ, and rcosθ = x, so then you have r + x = 5, and then r is equal to the square root of x^2 + y^2 so....square root of (x^2 + y^2) + x = 5....best I can do :/

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According to the equations to transform polar to rectangular coordinates

x = Cos(theta)
y = r(sin)(theta)
r = sqrt(x^2+y^2)
So the original equation can be set as:

r+ rCos(theta) = 5
Making substitutions:
sqr(x^2+y^2) + x = 5
sqr(x^2+y^2) = 5-x
(x^2+y^2) = (5-x)^2
(x^2+y^2) = 25-10x+x^2
y^2 = 25-10x this is the answer.
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