An ellipse is rotated through a right angle in its own plane about its centre, which is fixed , prove that the locus of the point of intersection of a tangent to the ellipse in its original position with the tangent at the same point of the curve in its new position is
`( x^(2) + y^(2)) ( x^(2) + y^(2) - a^(2) - b^(2)) = 2 (a^(2) - b^(2)) xy`

An ellipse x^2+4y^2 =4 is rotated anticlockwise through a right angle in its own plane about its centre. If the locus of the point of intersection of a tangent to ellipse in its origin position with the tangent at the same point of the ellipse in its new position is given by the curve (x^2+y^2)^2=lambda(x^2+y^2)+mu xy where lambda and mu are positve integers. Find the value of (lambda+mu)

the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

The locus of the point of intersection of perpendicular tangents to the ellipse (x - 1)^2/16 + (y-2)^2/9= 1 is

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

The point of intersection of the two tangents to the ellipse the 2x^(2)+3y^(2)=6 at the ends of latus rectum is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , 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

The line 2x+y=3 intersects the ellipse 4x^(2)+y^(2)=5 at two points. The point of intersection of the tangents to the ellipse at these point is

Find the locus of the point of intersection of the perpendicular tangents of the curve y^(2)+4y-6x-2=0