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The two curves {x}^{{3}}-{3}{x}{y}^{{2}}+{2}={0} and {3}{x}^{{

Question

The two curves $x^{3} - 3 x y^{2} + 2 = 0$ and $3 x^{2} y - y^{3} - 2 = 0$

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The two curves

x^{3} - 3 x y^{2} + 2 = 0

and

3 x^{2} y - y^{3} - 2 = 0

6 mins ago

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Practice questions from similar books

Question 1

Prove that

y = \frac{4 sin θ}{( 2 + cos θ )} - θ

is an increasing function in

[0, \frac{π}{2}] ˙

View solution

Question 2

Statement 1: An equation of a common tangent to the parabola

y^{2} = 163 x

and the ellipse

2 x^{2} + y^{2} = 4 i s y = 2 x + 23

.Statement 2: If the line

y = m x + \frac{4 3}{m}, (m \neq = 0)

is a common tangent to the parabola

y^{2} = 163 x

and the ellipse

2 x^{2} + y^{2} = 4

, then m satisfies

m^{4} + 2 m^{2} = 24

View solution

Question 3

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is

\frac{π}{3} ˙

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Question 4

A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is

(a^{\frac{2}{3}} + b^{\frac{2}{3}})^{\frac{3}{2}}

View solution

Question Text

The two curves

x^{3} - 3 x y^{2} + 2 = 0

and

3 x^{2} y - y^{3} - 2 = 0

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The two curves x3−3xy2+2=0 and 3x2y−y3−2=0

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Practice questions from similar books

The two curves $x^{3} - 3 x y^{2} + 2 = 0$ and $3 x^{2} y - y^{3} - 2 = 0$