If a function is represented parametrically by the equations `x=(1+log_(e)t)/(t^(2)),y=(3+ 2 log_(e)t)/(t),` then which of the following statements are true ?

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? y^(x-2x y^(prime))=y y y^(prime)=2x(y^(prime))^2+1 x y^(prime)=2y(y^(prime))^2+2 y^(y-4x y^(prime))=(y^(prime))^2

The focus of the conic represented parametrically by the equation y=t^(2)+3, x= 2t-1 is

f(x)=int_(e^(x))^(e^(-x))ln((1)/(t))dt , then which of following are correct?

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof(dy)/(dx)-x((dy)/(dx))^3 is__________

Let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true?

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof|(dy)/(dx)-x((dy)/(dx))^3| is__________

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof|(dy)/(dx)-x((dy)/(dx))^3| is__________

A curve is represented parametrically by the equations x = e^t cos t and y = e^t sin t where t is a parameter. Then The relation between the parameter 't' and the angle a between the tangent to the given curve andthe x-axis is given by, 't' equals

A curve is represented parametrically by the equations x=e^(1)cost andy=e^(1) sin t, where t is a parameter. Then, If F(t)=int(x+y)dt, then the value of F((pi)/(2))-F(0) is

A curve is represented parametrically by the equations x=t+e^(at) and y=-t+e^(at) when t in R and a > 0. If the curve touches the axis of x at the point A, then the coordinates of the point A are