Find the points on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` such that the tangent at each point makes equal angles with the axes.

Find the points on the ellipse 4x^(2)+9y^(2)=36 at which the tangents are paralle to x-axis.

Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^(2))=2 at the point (a,b).

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

If eccentric angle of a point lying in the first quadrant on the ellipse x^2/a^2 + y^2/b^2 = 1 be theta and the line joining the centre to that point makes an angle phi with the x-axis, then theta - phi will be maximum when theta is equal to

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

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.

If the tangent at any point on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 intersects the coordinate axes at P and Q , then the minimum value of the area (in square unit ) of the triangle OPQ is (O being the origin )-

The eccentric angles of the two points P and Q on the ellipse x^2/a^2+y^2/b^2=1(a>b) are theta and phi resp.If the chord PQ makes angle 90^@ with the vertex (a,0)of the ellipse then show that tan(theta/2)tan(phi/2)=-b^2/a^2

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find l .

The sum of the squares of the perpendiculars on any tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from two points on the minor axis each at a distance a e from the center is (a) 2a^2 (b) 2b^2 (c) a^2+b^2 (d) a^2-b^2