wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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(9) and one point(1,3)

y - 3 = 9(x-1)

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

-3 = 9 (x-1)

x=23

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

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

This is given as ‘a’ in the question. We get 9a2=82


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometrical Interpretation of a Derivative
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon