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Question

The number of points on the curve x3/2+y3/2=a3/2, where the tangents are equally inclined to the axes, is

A
2
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B
1
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C
0
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D
4
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Solution

The correct option is B 1
If the tangents are equally inclined to the axes we get yx,y=1.
Therefore
32x+32y.y=0

y=1 implies
x+y=0

x=y

x=y.
x1=y1.
Substituting in the equation we get
2x32=a32

x=a223
Therefore
(x1,y1)=(a223,a223)
Therefore there exists only one point.

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