Question

The locus of the mid point of the portion between the axes of xcosa+ysina=pwhere p is constant is

Answer 1

Hey

$x \cos( \alpha ) + y \sin( \alpha ) = p$

Well, let's play with what we have ^^

$\frac{x}{p \sec( \alpha ) } + \frac{y}{ \csc( \alpha ) } = 1$

(•) Reminds of something ? ( Intercept Form )

$x - intercept : p \sec( \alpha )$

$y - intercept : p \csc( \alpha )$

Fortunately,

$mid - point :( \frac{p \sec \alpha}{2} , \frac{p \csc \alpha }{2} )$

(•) Beats me ^^" The Equation resembles :

$\frac{1}{ {x}^{2} } + \frac{1}{ {y}^{2} } = \frac{4}{ {p}^{2} }$
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=_= Haww Question's over ! The locus is as given at last !

✓✓ Have a Great Day Buddy

^_^ Ansh