0

Guest

Courses New

Find the area of the triangle formed by the positive x-axis and the tangent and normal to the curve x2+y2=9 at (2,√5)

Find the area of the triangle formed by the positive x-axis and the tangent and normal to the curve x2+y2=9 at (2,√5)

Grade:12th pass

1 Answers

Susmita
425 Points
5 years ago
Given x2+y2=9. This is circle of radius 3 with centre at origin (0,0).
For equation of tangent,we have to calcute dy/dx.
From the given equation
y2=9-x2
Differentiate both sides wrt x
2y(dy/dx)=-2x
or,dy/dx=-x/y
dy/dx at the point (2,root 5) is
\frac{dy}{dx}=\frac{-x}{y}=\frac{-2}{\sqrt{5}}
So equation of tangent
Y-y=m(X-x)
Or,Y-\sqrt{5} = \frac{-2}{\sqrt{5}}(X-2)
Or,Y= \frac{-2x}{\sqrt{5}} +\frac{9}{\sqrt{5}}
This tangent intersect the positive x axis at a point where Y=0,ie,
X=9/2=4.5
As the curve is a circle,so the normal at (2,root5) will be the radius drawn from (2,root5) to centre (0,0).
Please draw a triangle with vertices at (0,0),(4.5,0),(2,root5).
Now drop a straight line from (2,root5) to (2,0).This line will divide the triangle into two sections.
For the 1st section,the base length is 2 and height is root5.So area is (1/2)*2*root5=root5.
For the second segment,base length is (4.5-2)=2.5 and height is root5.So area is (1/2)*2.5*root5=9root5/4.
Add up these two area and that is the final answer.
Ask me if you face any difficulty with my instruction.
If you are helped please approve the answer.

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More