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Question Number 51612 by peter frank last updated on 29/Dec/18

F i n d t h e e q u a t i o n o f

t h e e l l i p s e w i t h e c e n t r i c i t y

\frac{1}{2} a n d t h e f o c u s (2, 1)

D o e s t h e l i n e x = 3 t o u c h e s

e l l i p s e . i f s o a t w h a t

p o i n t ? i f l i n e x = 5 i s t h e

l i n e o f d i r e c t i o n .

Answered by tanmay.chaudhury50@gmail.com last updated on 29/Dec/18

Answered by peter frank last updated on 29/Dec/18

\frac{P S}{P M} = e

e = \frac{1}{2}

P = (x, y)

S = (2, 1)

M = (5, y) \Rightarrow d i r e c t r i x

P S = \sqrt{{(x - 2)}^{2} + {(y - 1)}^{2}}

P M = \sqrt{{(x - 5)}^{2} + (y - y)}

\frac{P S}{P M} = \frac{1}{2}

3 x^{2} + 4 y^{2} - 6 x - 8 y - 5 = 0

x = 3

y^{2} - 2 y + 1 = 0

f r o m

b^{2} = 4 a c

{(- 2)}^{2} = 4

h e n c e x = 3 t o u c h e s t h e

e l l i p s e