The locus of the point which divides the double ordinates of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` in the ratio `1:2` internally is

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

The locus of the point of intersection of two perpendicular tangents to the ellipse (x^(2))/(9) +(y^(2))/(4)=1 is -

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 forms a triangle of constant area with the coordinate axes is (a) straight line (b) a hyperbola (c) an ellipse (d) a circle

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

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.

Show tht the locus of the middle points of chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 drawn through an extremity of the minor axis is (x^(2))/(a^(2))+(y^(2))/(b^(2)) = pm (y)/(b)

Find the co-ordinate of that point which divides the line segment joining the points (-2, 5, 1) and (3.-5, 6) in the ratio 3 : 2 internally.

Find the locus of the point which is equidistant from the points A(0,2,3) & B(2,-2,1)

Find the coordinates of the point which divides the line segment joining the points (a + b, a - b) and (a - b, a + b) in the ratio 3 : 2 internally

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.