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 coordinates of those points on the ellipse x^2/a^2 + y^2/b^2 = 1 , tangents at which make equal angles with the axes. Also prove that the length of the perpendicular from the centre on either of these is sqrt((1/2)(a^2+b^2)

If the tangent at any point of the ellipse (x^2)/(a^3)+(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)

The parametric angle alpha where -piltalphalepi of the point on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 at which the tangent drawn cuts the intercept of minimum length on the coordinates axes, is/are

Find the locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 form a triangle of constant area with the coordinate axes.

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 .

Tangent at a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is drawn which cuts the coordinates axes at A and B the minimum area of the triangle OAB is ( O being origin )

Find the equations of the tanggents to the ellipse (x ^(2))/(2) + (y ^(2))/(7) =1 that make an angle of 45 ^(@) with the x-axis.

If p(theta) is a point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtb) then find its coresponding point

The distance of the center of the ellipse x^(2)+2y^(2)-2=0 to those tangents of the ellipse which are equally inclined to both the axes is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , which make complementary angles with x - axis, is