If-the-line-y-mx-c-is-a-tangent-of-a-circle-x-2-y-2-r-2-Show-that-c-2-r-2-1-m-2-

Question Number 170458 by MathsFan last updated on 24/May/22

I f t h e l i n e y = m x + c i s a t a n g e n t o f

a c i r c l e x^{2} + y^{2} = r^{2} . S h o w t h a t,

c^{2} = r^{2} (1 + m^{2})

Answered by greougoury555 last updated on 24/May/22

\Rightarrow r = \frac{∣ c ∣}{\sqrt{1 + m^{2}}}

\Rightarrow r^{2} = \frac{c^{2}}{1 + m^{2}}

\Rightarrow c^{2} = (1 + m^{2}) r^{2}

Commented by MathsFan last updated on 24/May/22

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