Show-that-the-locus-of-a-point-which-moves-so-that-its-distance-from-the-point-ae-0-is-e-times-its-distance-from-the-line-x-a-e-is-given-by-the-equation-x-2-a-2-y-2-a-2-1-e-2-1-

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Question Number 51271 by peter frank last updated on 25/Dec/18

$$Showthatthelocusofa$$$$pointwhichmovesso$$$$thatitsdistancefrom$$$$thepoint(ae,0)isetimes$$$$itsdistancefromthe$$$$linex=\frac{a}{e}isgivenbythe$$$$equation$$$$\frac{x^2}{a^2}+\frac{y^2}{a^2(1-e^2)}=1$$$$$$

Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18

$$\sqrt{{(x-ae)}^2+y^2}=e(x-\frac{a}{e})$$$$\sqrt{{(x-ae)}^2+y^2}=(ex-a)$$$$x^2-2xae+a^2{e}^2+y^2=e^2{x}^2-2xae+a^2$$$$x^2(1-e^2)+y^2=a^2(1-e^2)$$$$\frac{x^2}{a^2}+\frac{y^2}{a^2(1-e^2)}=1$$$$$$

Commented by peter frank last updated on 25/Dec/18

$$muchrespectmrtanmay.$$$$GODblessyou.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18

$$thankyou\dots$$

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