Prove that the equation of tangent of the ellipse `x^(2)/a^(2)+y^(2)/b^(2) = 1" at point "(x_(1),y_(1))" is (xx_(1))/a^(2) + (yy_(1))/b^(2)=1`.

Find the equations of tangent and normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,y_1)

Find the equations of tangent and normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,y_1)

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

Find the equation of the tangent to the curve (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,\ y_1) on it.

Find the equations of the tangent drawn to the ellipse (x^(2))/(3) + y^(2) =1 from the point (2, -1 )

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

For the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 and (x^(2))/(b^(2))+(y^(2))/(a^(2)) =1

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2= at the points where it is intersected by the line 2x+3y=1 . The point of intersection of these tangents is (8, 6). Statement 2 : The equation of the chord of contact to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from an external point is given by (xx_1)/(a^2)+(y y_1)/(b^2)-1=0

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is