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Question Number 74817 by peter frank last updated on 01/Dec/19

	Answered by mr W last updated on 03/Dec/19

	$p a r a l l e l c h o r d s :$ $y = m x + k$ $x (m x + k) = c^{2}$ ${m x}^{2} + k x - c^{2} = 0$ $x_{1} + x_{2} = - \frac{k}{m}$ $x_{1} x_{2} = - \frac{c^{2}}{m}$ $m i d d l e p o i n t o f c h o r d : M (p, q)$ $p = \frac{x_{1} + x_{2}}{2} = - \frac{k}{2 m}$ $q = \frac{y_{1} + y_{2}}{2} = \frac{c^{2}}{2} (\frac{1}{x_{1}} + \frac{1}{x_{2}}) = \frac{c^{2} (x_{1} + x_{2})}{2 x_{1} x_{2}} = \frac{k}{2}$ $\Rightarrow q = - m p$ $\Rightarrow y = - m x \leftarrow e q n . o f l o c u s$
	Commented by peter frank last updated on 06/Dec/19

	$t h a n k y o u$
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