F i n d space t h e space e q u a t i o n space o f space t h e space p a r a b o l a space w h o s e space f o c u s space i s space left parenthesis 1 comma 1 right parenthesis space a n d space t h e space d i r e c t r i x space i s space t h e space
l i n e space p a r a l l e l space t o space 2 x plus 3 y minus 9 equals 0 space a n d space space p a s s e s space t h r o u g h space left parenthesis 3 comma 4 right parenthesis.

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Asked by Topperlearning User | 15th Nov, 2016, 10:44: PM

Expert Answer:

L i n e space p a r a l l e l space t o space 2 x plus 3 y minus 9 equals 0 space w i l l space b e space 2 x plus 3 y plus k equals 0
G i v e n space t h a t space space 2 x plus 3 y plus k equals 0 space space space p a s s e s space t h r o u g h space left parenthesis 3 comma 4 right parenthesis space s o
6 plus 12 plus k equals 0 rightwards double arrow k equals negative 18
S o space t h e space d i r e c t r i x space i s space 2 x plus 3 y minus 18 equals 0
F o c u s space i s space left parenthesis 1 comma 1 right parenthesis
L e t space u s space c o n s i d e r space a space p o i n t space P left parenthesis x comma y right parenthesis space n o w space t h e space p a r a b o l a space i s space t h e space l o c u s space o f space P space t h a t space m o v e s space i n space a space p l a n e space
s u c space t h a t space i t s space d i s tan c e space f r o m space f o c u s space i s space e q u a l space t o space t h e space d i s tan c e space f r o m space d i r e c t r i x.
E q u a t i o n space o f space t h e space p a r a b o l a space i s space g i v e n space b y
left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals open parentheses fraction numerator 2 x plus 3 y minus 18 over denominator square root of 2 squared plus 3 squared end root end fraction close parentheses squared
rightwards double arrow x squared plus y squared minus 2 x minus 2 y plus 2 equals fraction numerator 4 x squared plus 9 y squared plus 324 plus 12 x y minus 108 y minus 72 x over denominator 13 end fraction
rightwards double arrow 9 x squared plus 4 y squared plus 46 x plus 82 y minus 12 x y minus 298 equals 0

Answered by  | 16th Nov, 2016, 12:44: AM