The number of point(s) (x, y) (where x and y both are perfect squares of integers) on the parabola $y^{2} = p x$ , p being a prime number, is

zero

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one

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two

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infinite

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Solution

The correct option is B one
If x is a perfect square, then px will be a perfect square only if p is a perfect square, which is not possible as p is a prime number. Hence y cannot be a perfect square. So number of such points will be only one (0, 0)

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