If a hyperbola be rectangular, and its equation be `xy = c^2,` prove that the locus of the middle points of chords of constant length 2d is `(x^2+y^2)(xy-c^2)=d^2 xy.`

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-

Find dy/dx when (x^2 +y^2))^2 = xy

Find the equation of a curve passing through (2,1) if the slope of the tangent to the curve at any point (x,y) is (x^2+y^2)/(2xy)

From the points on the circle x^(2)+y^(2)=a^(2) , tangents are drawn to the hyperbola x^(2)-y^(2)=a^(2) : prove that the locus of the middle-points (x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))

If there are two points A and B on rectangular hyperbola xy=c^2 such that abscissa of A = ordinate of B, then locusof point of intersection of tangents at A and B is (a) y^2-x^2=2c^2 (b) y^2-x^2=c^2/2 (c) y=x (d) non of these

A, B, C are three points on the rectangular hyperbola xy = c^2 , The area of the triangle formed by the points A, B and C is

Solve the differential equations: x^2y'=x^2+xy+y^2

Solve : (x^2-xy)dy+(3xy+y^2)dx=0 .

Show that : (5xy +3y)^2 - (5xy-3y)^2 = 60 xy^2 .

If the normal to the rectangular hyperbola xy = c^2 at the point 't' meets the curve again at t_1 then t^3t_1, has the value equal to