If the tangents to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` make angles `alphaa n dbeta` with the major axis such that `tanalpha+tanbeta=gamma,` then the locus of their point of intersection is (a) `x^2+y^2=a^2` (b) `x^2+y^2=b^2` (c) `x^2-a^2=2lambdax y` (d) `lambda(x^2-a^2)=2x y`

Extremities of the latera recta of the ellipses (x^2)/(a^2)+(y^2)/(b^2)=1(a > b) having a given major axis 2a lies on

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.

The line y=x+lambda is tangent to the ellipse 2x^(2)+3y^(2)=1 , then lambda is-

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

If y=mx+c is the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at any point on it, show that c^(2)=a^(2)m^(2)+b^(2). Find the coordinates of the point of contact.

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be (a) x^2+y^2=6 (b) x^2+y^2=9 x^2+y^2=3 (d) x^2+y^2=18

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0 .

The line y=x+lambda is tangent to the ellips 2x^2+3y^2=1 Then lambda is