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

Question

Jitender Singh · Answer

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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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

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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 orthogonallyy=x^3 and 6y=7 – x^2

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TANGENTS AND NORMALS

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