The locus of a point reprersented by `x=a/2((t+1)/t),y=a/2((t-1)/1)` , where `t in R-{0},` is `x^2+y^2=a^2` (b) `x^2-y^2=a^2` `x+y=a` (d) `x-y=a`

Show that the locus represented by x=(1)/(2)a(t+(1)/(t)),y=(1)/(2)a(t-(1)/(t)) is a rectangular hyperbola.

The locus of the moving point whose coordinates are given by (e^t+e^(-t),e^t-e^(-t)) where t is a parameter, is (a) x y=1 (b) x+y=2 (c) x^2-y^2=4 (d) x^2-y^2=2

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (x^2-y^2)=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

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

A function y=f(x) is given by x=1/(1+t^2) and y=1/(t(1+t^2)) for all tgt0 then f is

If points Aa n dB are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2)) " then " (dy)/(dx) is

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

Let P be any moving point on the circle x^2+y^2-2x=1. A B be the chord of contact of this point w.r.t. the circle x^2+y^2-2x=0 . The locus of the circumcenter of triangle C A B(C being the center of the circle) is 2x^2+2y^2-4x+1=0 x^2+y^2-4x+2=0 x^2+y^2-4x+1=0 2x^2+2y^2-4x+3=0

Let P be any moving point on the circle x^2+y^2-2x=1. A B be the chord of contact of this point w.r.t. the circle x^2+y^2-2x=0 . The locus of the circumcenter of triangle C A B(C being the center of the circle) is 2x^2+2y^2-4x+1=0 x^2+y^2-4x+2=0 x^2+y^2-4x+1=0 2x^2+2y^2-4x+3=0