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

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that (t_2)^2geq8.

Normals drawn to the hyperbola xy=2 at the point P(t_1) meets the hyperbola again at Q(t_2) , then minimum distance between the point P and Q is

The normal at three points P, Q, R on a rectangular hyperbola intersect at a point T on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' is

The area formed by the normals to y^2=4ax at the points t_1,t_2,t_3 is

Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four points, three of them being (2, 2), (4, 1) and (6,2/3), then the coordinates of the fourth point are (1/4,16) . Statement 2 : If a circle S=0 intersects a hyperbola x y=c^2 at t_1,t_2,t_3, and t_4 then t_1t_2t_3t_4=1

Find the equations of the normal to the given curves at the indicated points: x = cost, y = sin t at t = pi/4

Find the equations of the tangent and normal to the parabola y^2=4a x at the point (a t^2,2a t) .

The slope of the tangent to the curve x = t^2+3t-8, y = 2t^2-2t-5 at the point (2,-1) is:

Find the area of the region bounded by the curve x=a t^2,y=2a t between the ordinates corresponding t=1a n dt=2.