The equation of curve referred to the new axes, axes retaining their directions, and origin `(4,5)` is `X^2+Y^2=36` . Find the equation referred to the original axes.

The equation of the normal to the curve y^(4)=ax^(3) at (a, a) is

The equation of the normal to the curve y^2=4ax at point (a,2a) is

The equation of the normal to the curve y^(4)=ax^(3) at (a,a) is

The equation of the normal to the curve y^2=4ax having slope m

The equation of a curve referred to a given system of axes is 3x^(2)+2xy+3y^(2)=10 .Find its equation if the axes are rotated through an angle 45^(@) ,the origin remaining unchanged.

The equation of hyperbola referred to its axes as axes of coordinate whose distance between the foci is 20 and eccentricity equals sqrt2 is

The co-ordinate axes are rotated about the origin O in the counter-clockwise direction through an angle 60^(@) If a and b are the intercepts made on the new axes by a straight line whose equation referred to the original axes is 3x + 4y = 5 , then (1)/(a^(2)) + (1)/(b^(2)) =

The co-ordinate axes are rotated about the origin O in the counter-clockwise direction through an angle 60^(@) If p and q are the intercepts made on the new axes by a straight line whose equation referred to the original axes is x + y = 1 , then (1)/(p^(2)) + (1)/(q^(2)) =

The equation of a curve referred to a given system of axes is 3x^(2)+2xy+3y^(2)=10 . The transformed equation of the curve. If the axes are rotated about the origin through an angle 45^(@) is 2x^(2)+y^(2)=k then k=