The length of LR of the parabola 25[(x-1)]² + (y-3)²] = [4x-3y+15]² is blank to the power of blankblank to the power of blank

Asked by Malavika Umesh | 9th May, 2015, 08:11: PM

Expert Answer:

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 r e minus w r i t t e n space a s space open parentheses x minus 1 close parentheses squared plus open parentheses y minus 3 close parentheses squared equals open parentheses fraction numerator 4 x minus 3 y plus 15 over denominator square root of 4 squared plus 3 squared end root end fraction close parentheses squared F r o m space t h i s space f o r m comma space w e space g e t 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 a s space open parentheses 1 comma 3 close parentheses E q u a t i o n space o f space t h e space d i r e c t r i x space o f space t h e space p a r a b o l a space i s space 4 x minus 3 y plus 15 equals 0 T h e space d i s tan c e space b e t w e e n space f o c u s space a n d space t h e space d i r e c t r i x space i s space open vertical bar fraction numerator 4 cross times 1 minus 3 cross times 3 plus 15 over denominator square root of 4 squared plus 3 squared end root end fraction close vertical bar equals 2 T h i s space i s space c a l l e d space f o c a l space p a r a m e t e r space apostrophe 2 a apostrophe space o f space a space p a r a b o l a. T h e space l e n g t h space o f space l a t u s space r e c t u m space i s space 2 space t i m e s space t h e space f o c a l space p a r a m e t e r. H e n c e comma space l e n g t h space o f space l a t u s r e c t u m space i s space 2 cross times 2 equals 4.

Answered by satyajit samal | 11th May, 2015, 11:52: AM