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Analytical Geometry> How does find the slope of a circle. Plea...

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How does find the slope of a circle. Please give me an easy method which works all the time.Thanks

Jai Mahajan , 10 Years ago

Grade 12

1 Answers

Sumit Majumdar

Last Activity: 10 Years ago

Dear student,
We know that atany pointP having the coordinates (x,y)on the unit circle satisfies the relation
$x^{2}+y^{2}=1$
Hence, we get that
$2x+2y\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=-\frac{x}{y}$
Now we can use the usual parameterization of the circle, i.e. x=cos(θ)andy=sin(θ), the slope at a givenθis given by
Slope atθ is given by:
$\frac{dy}{dx}=-\frac{x}{y}=-\frac{cos\theta }{sin\theta}$
Regards
Sumit

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