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 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

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 eccentricity of the hyperbola given by equations x=(e^t+e^(-1))/2a n dy=(e^t-e^(-1))/3,t in Rdot

Find the eccentricity of the hyperbola given by equations x=(e^t+e^(-1))/2a n dy=(e^t-e^(-1))/3,t in Rdot

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

The equation of straight line passing through (-a ,0) and making a triangle with the axes of area T is (a) 2T x+a^2y+2a T=0 (b) 2T x-a^2y+2a T=0 (c) 2T x-a^2y-2a T=0 (d)none of these

If e and e' are the eccentricities of the hyperbola x^2/a^2-y^2/b^2=1 and y^2/b^2-x^2/a^2=1, then the point (1/e,1/(e')) lies on the circle (A) x^2+y^2=1 (B) x^2+y^2=2 (C) x^2+y^2=3 (D) x^2+y^2=4

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

The point of intersection of the tangent at t_(1)=t and t_(2)=3t to the parabola y^(2)=8x is . . .

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y