Find the points on the ellipse `(x^2)/4+(y^2)/9=1` on which the normals are parallel to the line `2x-y=1.`

Find the points on the curve y = x^(3) -6x^(2) + x + 3 where the normal is parallel to the line x + y = 1729

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

Find the point on the curve y=x^(3)-6x^(2)+x+3 where the normal is parallel to the line x + y = 1729.

Find points on the curve (x^(2))/(4) +(y^(2))/(25) =1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.

A point on the ellipse x^2+3y^2=37 where the normal is parallel to the line 6x-5y=2 is (5,-2) (b) (5, 2) (c) (-5,2) (d) (-5,-2)

Find the point on the curve y=x^(2)-5x+4 at which the tangent is parallel to the line 3x + y = 7.

Find points on the curve (x^(2))/(9) +(y^(2))/(16) =1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.

Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).