1. find the eqation of tangent to curve 3x2-y2=8 which passthrough point 4/3,0

Asked by sonalchoudhary882 | 22nd Oct, 2018, 12:22: AM

Expert Answer:

E q u a t i o n space o f space space g i v e n space c u r v e space i s space 3 x squared minus y squared equals 8 comma space w e space h a v e space t o space f i n d space t h e space e q u a t i o n space o f space a space tan g e n t.
f i r s t space t h i n g space t r y space t o space r e c a l l space space t h a t space tan g e n t space i s space a space l i n e space s o space f i n d i n g space t h e space e q u a t i o n space o f space a space tan g e n t space m e a n s space w e space h a v e space t o space f n d space t h e space e q u a t i o n space o f space t h e space l i n e.
T h e r e space a r e space d i f f e r e n t space f o r m s space o f space a space e q u a t i o n space o f space l i n e. space w e space u s e space s l o p e space p o i n t space f o r m.
S l o p e space space p o i n t space f o r m space i s space y minus y subscript 1 equals m left parenthesis x minus x subscript 1 right parenthesis space w h e r e space m space i s space t h e space s l o p e space. space W e space a l r e a d y space h a v e space p o i n t space left parenthesis 4 over 3 comma 0 right parenthesis space w e space h a v e space t o space f i n d space s l o p e.
s o space d e r i v a t i v e space a t space p o i n t space i s space n o t h i n g space b u t space t h e space s l o p e space o f space tan g e n t space a t space t h a t space p o i n t.
space 3 x squared minus y squared equals 8
d i f f e r e n t i a t e space w. r. t space
w e space g e t space 6 x minus 2 y fraction numerator d y over denominator d x end fraction equals 0
2 y fraction numerator d y over denominator d x end fraction equals 6 x
fraction numerator d y over denominator d x end fraction equals fraction numerator 6 x over denominator 2 y end fraction equals fraction numerator 3 x over denominator y end fraction
n o w space s u b s t i t u t i n g space left parenthesis 4 over 3 comma 0 right parenthesis space i n space a b o v e space e q u a t i o n space w e space g e t space fraction numerator d y over denominator d x end fraction equals infinity comma space i. e comma space s l o p e space i s space i n f i n i t y
s o space l i n e space i s space p e r p e n d i c u l a r space t o space X space minus a x i s.
h e n c e space tan g e n t space i s space p a r a l l e l space t o space Y minus a x i s space c u t t i n g space X minus a x i s space a t space 4 over 3 comma
space h e n c e space e q u a t o n space o f space tan g e n t space i s space x equals 4 over 3 space i. e comma space 3 x minus 4 equals 0.

Answered by Ram Singh | 22nd Oct, 2018, 07:16: PM