Q. 385.0( 2 Votes )

The equation of n A. 3x – y = 8

B. 3x + y + 8 = 0

C. x + 3y ± 8 = 0

D. x + 3y = 0

Answer :

Given the equation of the line is 3x2 – y2 = 8


Now differentiating both sides with respect to x, we get



Now applying the sum rule of differentiation and differentiation of constant =0, so we get



Taking out the constants we get



Applying the power rule of differentiation we get






So this is the slope of the given curve.


We know the slope of the normal to the curve is




Now given the equation of the line x + 3y = 8


3y=8-x


Differentiation with respect to x, we get





So the slope of the line is


Now as the normal to the curve is parallel to this line, hence the slope of the line should be equal to the slope of the normal to the given curve,



3y=3x


y=x


On substituting this value of the given equation of the curve, we get


3x2 – y2 = 8


3x2 – (x)2 = 8


2x2 = 8


x2 = 4


x=± 2


When x=2, the equation of the curve becomes,


3x2 – y2 = 8


3(2)2 – y2 = 8


3(4) – y2 = 8


12-8= y2


y2 = 4


y=±2


When x=-2, the equation of the curve becomes,


3x2 – y2 = 8


3(-2)2 – y2 = 8


3(4) – y2 = 8


12-8= y2


y2 = 4


y=±2


So, the points at which normal is parallel to the given line are (±2, ±2).


And required equation of the normal to the curve at (±2, ±2) is



3(y-(±2))=-(x-(±2))


3y-(±6)=-x+(±2)


x+3y-(±6)-(±2)=0


x+3y+(± 8)=0


Hence the equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is x+3y+(± 8)=0.


So the correct option is option C.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the equationRD Sharma - Volume 1

Find the equationMathematics - Board Papers

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the conditioMathematics - Exemplar