Q. 28

# Show that the cur

Answer :

If the two curve cut orthogonally then angle between their tangent at intersecting point is equal to 90⁰.

We have to find their intersecting point.

x3 – 3xy2 + 2 = 0 …(1) and 3x2y – y3 – 2 = 0 …(2)

On adding eq (1) and eq (2)

x3 – 3xy2 + 2 + 3x2y – y3 – 2 = 0

x3 – y3 – 3xy2 + 3x2y = 0

(x – y)3 = 0 x = y

Put x = y in eq (1)

y3 – 3y3 + 2 = 0 y = 1

At y = 1, x = 1 m1 at (1, 1) = 0 m2 at (1, 1) = -2/0

At (1, 1)   So, we can say that two curve cut each other orthogonally because angle between two tangent at their intersecting point is equal to 90⁰.

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