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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 , 11 Years ago
Grade 12
anser 1 Answers
Sumit Majumdar
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
Last Activity: 11 Years ago
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