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Womble548
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#1
Report Thread starter 14 years ago
#1
Hi, I am stuck on this question. I think my working is right but I dont know if I can simplify my answer to match the correct answer.

Find equations of the tangent and normal to the ellipse with equation 4x^2 + 25y^2 = 100 at the point P(5cost, 2sint)

I get:

dy/dx = -8x/50y
At P, dy/dx = -2cott/5

The equation of the tangent is:
-2cott/5 = (y-2sint)/(x-5cost)
(-2xcost)/(5sint) + (2cos^2t)/(sint) = y-2sint

The answer should be xcost/5 + ysint/2 = 1

How do they get the equation to look so simple?

Havent attempted the normal yet, but thats pretty easy when you know how to do the tangent.
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JamesF
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Report 14 years ago
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(y - 2sint) = -2cot(t)/5 (x - 5cost)
y = 2sint + 2cos^2(t)/sin(t) - 2xcot(t)/5

Multiply by sin(t);
ysin(t) = 2sin^2(t) + 2cos^2(t) - 2xcos(t)/5
(sin^2 + cos^2 = 1), so

ysint = 2 - 2xcos(t)/5
ysint/2 + xcos(t)/5 = 1
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