CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

If the length of the tangent drawn at the point (1,3) on the curve y=3x3 is a, then find the value of 9a2


___


Open in App
Solution

Length of the tangent at a point is defined as the length of tangent between the given point and the point where it cuts x -axis. So, we will first find the tangent and find the point where it cuts the x-axis to find the length of the tangent.

We can find the slope of the tangent by taking derivative of y in the given equation

f(x)=9x2

f(1)=9

m=9

Now we will write the equation of tangent using slope as 9 and point as (1,3)

y3=9(x1)

To find the point where it cuts the x-axis, substitute y=0 in this

3=9(x1)

x=23

So the length of the tangent is the distance between the points (23,0) and (1,3)

=(13)2+32=(19)+9=829

This is given as ‘a’ in the question.

a2=82/9

Hence, 9a2=82


flag
Suggest Corrections
thumbs-up
1
BNAT
mid-banner-image