Please solve 

Asked by sanjaysingh.srct | 5th Sep, 2019, 12:46: PM

Expert Answer:

Equation of a line L1 is y plus 2 a t equals t left parenthesis x minus a t squared right parenthesis
S o comma space L subscript 1 colon y minus x t plus 2 a t plus a t cubed equals 0 space.... space left parenthesis i right parenthesis
T a k e space t space a s space minus 1 over t
S o comma space w e space h a v e space t h e space a n o t h e r space l i n e space a s
L subscript 2 colon space y plus 1 over t x minus fraction numerator 2 a over denominator t end fraction minus a over t cubed equals 0 space... space left parenthesis i i right parenthesis
C l e a r l y comma space L subscript 1 perpendicular L subscript 2
T o space f i n d space t h e space p o i n t space o f space i n t e r e c t i o n comma space l e t apostrophe s space s o l v e space e q n s space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis
W e space o b t a i n
x equals a open parentheses t squared plus 1 over t squared plus 1 close parentheses equals a open parentheses open parentheses t minus 1 over t close parentheses squared plus 3 close parentheses comma space y equals a open parentheses 1 over t minus t close parentheses
T a k e space t minus 1 over t equals p
rightwards double arrow x equals a left parenthesis p squared plus 3 right parenthesis space a n d space y equals a p rightwards double arrow p equals y over a
rightwards double arrow x equals a open parentheses y squared over a squared plus 3 close parentheses equals 1 over a y squared plus 3 a space w h i c h space i s space a space p a r a b o l a

Answered by Renu Varma | 19th Sep, 2019, 11:42: AM

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