Q)Tangents to y squared equals 8 x space a r e space i n c l i n e d space a t space 45 degree space t o space t h e space l i n e space y equals 3 x plus 5 space. space T h e space c o o r d i n a t e s space o f space t h e space p o i n t space o f space c o n t a c t space a r e
left parenthesis A right parenthesis left parenthesis 1 half comma 0 right parenthesis space space left parenthesis B right parenthesis open parentheses 1 half comma negative 2 close parentheses space space left parenthesis C right parenthesis open parentheses 1 half comma negative 3 close parentheses space space left parenthesis D right parenthesis open parentheses 8 comma 8 close parentheses space space space left parenthesis E right parenthesis open parentheses 18 comma negative 12 close parentheses

Asked by araima2001 | 24th Mar, 2017, 07:31: PM

Expert Answer:

begin mathsize 16px style Given space that space tangents space to space straight y squared equals 8 space straight x space are space inclined space at space 45 degree space to space the space line space straight y space equals space 3 straight x plus 5.
Using space the space slope space formula comma
tanθ equals open vertical bar fraction numerator straight m subscript 1 minus straight m subscript 2 over denominator 1 plus straight m subscript 1 straight m subscript 2 end fraction close vertical bar
rightwards double arrow tan 45 equals open vertical bar fraction numerator straight m minus 3 over denominator 1 plus 3 straight m end fraction close vertical bar
rightwards double arrow 1 equals open vertical bar fraction numerator straight m minus 3 over denominator 1 plus 3 straight m end fraction close vertical bar
rightwards double arrow fraction numerator straight m minus 3 over denominator 1 plus 3 straight m end fraction equals plus-or-minus 1
space rightwards double arrow fraction numerator straight m minus 3 over denominator 1 plus 3 straight m end fraction equals 1 space space or space space fraction numerator straight m minus 3 over denominator 1 plus 3 straight m end fraction equals negative 1
rightwards double arrow straight m minus 3 equals 1 plus 3 straight m space or space straight m minus 3 equals negative 1 minus 3 straight m
rightwards double arrow 2 straight m equals negative 4 space space or space 4 straight m equals 2
rightwards double arrow straight m equals negative 2 space or space straight m equals 1 half
Equation space of space the space tangent space with space slope space straight m equals negative 2 space or space straight m equals 1 half space to space the space parabola space is space given space by
straight y equals mx plus straight a over straight x space where space the space equation space of space teh space parabola space is space given space by space straight y squared equals 4 ax
In space this space case space straight a equals 2 comma space straight m equals negative 2 space or space straight m equals 1 half
So comma space the space equation space of space the space tangents space are space straight y equals negative 2 straight x minus 1 space and space straight y equals 1 half straight x plus 4.
Now space to space find space the space coordinates space of space the space point space of space contact space of space the space tangents comma
solve space the space equation space of space the space tangents space and space the space parabola space simultaneously.
For space the space tangent space straight y equals negative 2 straight x minus 1 space and space space straight y squared equals 8 straight x comma
you space will space get space straight y equals 1 half space and space straight x equals negative 2
For space the space tangent space straight y equals 1 half straight x plus 4 space and space space straight y squared equals 8 straight x comma
you space will space get space straight y equals 8 space and space straight x equals 8
So comma space the space points space would space be space open parentheses 1 half comma negative 2 close parentheses space and space left parenthesis 8 comma 8 right parenthesis. end style

Answered by Rebecca Fernandes | 24th Mar, 2017, 10:54: PM