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TANGENTS AND NORMALS show that the following set of curves intersect orthogonally y=x^3 and 6y=7 – x^2

TANGENTS AND NORMALS
 
show that the following set of curves intersect orthogonally
y=x^3 and 6y=7 – x^2

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello student,
Please find the answer to your question below


If the curves intersect orthogonally, then tangents at their points of intersection must be perpendicular
Curve 1:
y = x^3
Slope of tangent:
y' = 3x^2…............(1)
Curve 2:
6y = 7 - x^2
Slope of tangent:
6y' = - 2x
y' = \frac{-x}{3}..............(2)
(1)\times (2)
-x^2
Find point of intersection
6x3= 7 – x2
x = 1
So -x2is -1.
Hence proved.

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