Equation of parabola having it's focus at S(2, 0) and one extremity of it's latus rectam as (2, 3) is

Asked by Malavika Umesh | 9th May, 2015, 08:15: PM

Expert Answer:

S i n c e space t h e space f o c u s space o f space t h e space p a r a b o l a space i s space a t space left parenthesis 2 comma 0 right parenthesis space a n d space o n e space e n d space o f space l a t u s space r e c t u m space i s space a t space left parenthesis 2 comma space 3 right parenthesis. therefore t h e space a x i s space o f space t h e space p a r a b o l a space i s space x minus a x i s. S e m i minus l e n g t h space o f space t h e space l a t u s space r e c t u m space i s space 2 a equals left parenthesis 3 minus 0 right parenthesis equals 3 therefore a equals 3 over 2 therefore 4 a equals 6 H e n c e space t h e space v e r t e x space s h o u l d space b e space open parentheses 2 minus 3 over 2 close parentheses equals 1 half space u n i t space f r o m space t h e space l e f t space o r space a t space open parentheses 1 half comma 0 close parentheses T h e space v e r t e x space s h o u l d space b e space open parentheses 2 plus 3 over 2 close parentheses equals 7 over 2 u n i t s space f r o m space t h e space r i g h t space o r space a t space open parentheses 7 over 2 comma 0 close parentheses. I f space t h e space v e r t e x space i s space a t open parentheses 1 half comma 0 close parentheses comma space t h e n 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 i s space y squared equals 4 a open parentheses x minus 1 half close parentheses comma space sin c e space i t space o p e n s space t o space t h e space r i g h t. therefore space y squared equals 6 open parentheses x minus 1 half close parentheses I f space t h e space v e r t e x space i s space a t open parentheses 7 over 2 comma 0 close parentheses comma space t h e n 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 i s space y squared equals negative 4 a open parentheses x minus 7 over 2 close parentheses comma space sin c e space i t space o p e n s space t o space t h e space l e f t. therefore space y squared equals negative 6 open parentheses x minus 7 over 2 close parentheses 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 c a n space b e space space y squared equals 6 open parentheses x minus 1 half close parentheses space o r space space y squared equals negative 6 open parentheses x minus 7 over 2 close parentheses

Answered by Prasenjit Paul | 11th May, 2015, 11:51: AM