please sove the following question:
 

Asked by manasd | 24th Jan, 2017, 09:24: PM

Expert Answer:

begin mathsize 16px style The space equation space of space the space curve space is space straight y equals fraction numerator left parenthesis straight x minus 7 right parenthesis over denominator left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction rightwards double arrow straight y left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis equals straight x minus 7
So comma space straight y left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis minus straight x plus 7 equals 0
This space cuts space the space straight x minus axis space at space the space point comma space where space straight y equals 0. space Putting space straight y equals 0 space in space left parenthesis straight i right parenthesis comma space we space get
minus straight x plus 7 equals 0 rightwards double arrow straight x equals 7
So comma space the space point space of space contact space is space left parenthesis 7 comma 0 right parenthesis.
Differentiating space left parenthesis straight i right parenthesis space wrt space straight x comma space we space get
dy over dx left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis plus straight y left parenthesis 2 straight x minus 5 right parenthesis minus 1 equals 0
Putting space straight x equals 7 space and space straight y equals 0 space in space left parenthesis ii right parenthesis space comma space we space get
open parentheses dy over dx close parentheses subscript left parenthesis 7 comma 0 right parenthesis end subscript left parenthesis 7 minus 2 right parenthesis left parenthesis 7 minus 3 right parenthesis plus 0 left parenthesis 2 left parenthesis 7 right parenthesis minus 5 right parenthesis minus 1 equals 0
rightwards double arrow open parentheses dy over dx close parentheses subscript left parenthesis 7 comma 0 right parenthesis end subscript left parenthesis 7 minus 2 right parenthesis left parenthesis 7 minus 3 right parenthesis minus 1 equals 0 rightwards double arrow open parentheses dy over dx close parentheses subscript left parenthesis 7 comma 0 right parenthesis end subscript equals 1 over 20
So comma space the space equation space of space the space tangent space at space left parenthesis 7 comma 0 right parenthesis space is space straight y minus 0 equals open parentheses dy over dx close parentheses subscript left parenthesis 7 comma 0 right parenthesis end subscript left parenthesis straight x minus 7 right parenthesis
rightwards double arrow straight y equals 0 equals 1 over 20 left parenthesis straight x minus 7 right parenthesis rightwards double arrow straight x minus 20 straight y minus 7 equals 0
The space equation space of space the space normal space at space left parenthesis 7 comma 0 right parenthesis space is space straight y minus 0 equals negative 1 over open parentheses dy over dx close parentheses subscript left parenthesis 7 comma 0 right parenthesis end subscript left parenthesis straight x minus 7 right parenthesis
rightwards double arrow straight y minus 0 equals negative 20 left parenthesis straight x minus 7 right parenthesis
rightwards double arrow 20 straight x plus straight y minus 140 equals 0 end style

Answered by Rebecca Fernandes | 25th Jan, 2017, 09:59: AM

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