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

{:("List"-I,"List"-II),("The number of rational points on the ellipse" (x^(2))/(9)+(y^(2))/(4)=1,4),("The number of integral points on the ellipse" (x^(2))/(9)+(y^(2))/(4)=1,2),("The number of integral points on the ellipse" (x^(2))/(3)+(y^(2))/(1)=1,infty):}

Area of the ellipse x^(2)/9+y^(2)/4=1 is

If P(theta) and Q((pi)/(2)+theta) are two points on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 then find the locus of midpoint of PQ

If P(theta) and Q((pi)/(2)+theta) are two points on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 then find the locus of midpoint of PQ

If P(theta) and Q((pi)/(2)+theta) are two points on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 then find the locus of midpoint of PQ

Find the equation of tangent to the ellipse (x^(2))/( 4) + (y^(2))/( 2) = 1 that perpendicular to the line y = x + 1 . Also, find the point of contact .

Find the area of smaller region bounded by the ellipse x^2/9 + y^2/4 = 1 and straight line x/3 + y/2 = 1 .

Find the area of the smaller region bounded by the ellipse (x^2 )/(9) + (y^2)/(4)=1 and the line (x)/(3) + (y )/(2) =1

Find the sum of the focal distance of any point on the ellipse 4x^2+9y^2=36 .

Find the area of the ellipse x^2/9 + y^2/16 = 1 .