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The number of points (x,y) (where x and y both are perfect squares of integers) on the parabola y^2=px,p being a prime number, is ?

The number of points (x,y) (where x and y both are perfect squares of integers) on the parabola y^2=px,p being a prime number, is ?

Grade:12

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
y2= px
y = sqrt(px)
Since x & y are perfect square integers, sqrt(x) is an integer.
Since p is a prime no., sqrt(p) is an irrational no.
The point  which satisfies the given condition is only (0, 0).
The no. of points is 1.
 
 
 

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