Home
Class 12
MATHS
Find the number of rational points on th...

Find the number of rational points on the ellipse `(x^2)/9+(y^2)/4=1.`

Text Solution

Verified by Experts

`(x^(2))/(9)+(y^(2))/(4)=1`
Let any point on the ellipse be `(3 cos theta, 2 sin theta)`
Sicne `sin theta and cos theta` can be rational for inifinitely many values of `theta epsi [0, 2pi]` , there infinite points.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

Find the area of the region bounded by the ellipse x^(2)/4+y^(2)/9=1 .

Find the coordinates of a point on the ellipse x^(2) + 2y^(2) = 4 whose eccentric angle is 60^(@)

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

Find the area of the region bounded by the ellipse x^(2)/16+y^(2)/9=1 .

Find the locus of middle points of chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which subtend right angle at its center.

Find the sum of the focal distance of any point on the ellipse 9x^(2) +25y^(2) = 225 .

If the coordinates of a point lies on the ellipse 9x^(2) + 16y^(2) = 144 be (2 , (3sqrt(3))/(2)) , find the eccentric angle of that point .

Find the the co-ordinates of the point on the ellipse x^2 + 2y^2 =4 whose eccentric angle is 60^@ .

Find the locus of middle points of chords of the ellipse x^2/a^2+y^2/b^2=1 which subtend right angles at its centre.