Area enclosed by the curve `y=f(x)` defined parametrically as `x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2)` is equal

Find the derivatives of the following : x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2))

Find the derivatives of the following : x = (1-t^2)/(1+t^2), y = (2t)/(1+t^2)

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

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

Find Distance between the points for which lines that pass through the point (1, 1) and are tangent to the curve represent parametrically as x = 2t-t^2 and y = t + t^2

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=y(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta) y(t)x'(t)dt, S=int_(alpha)^(beta) x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. If the curve given by parametric equation x=t-t^(3), y=1-t^(4) forms a loop for all values of t in [-1,1] then the area of the loop is

The equation of the normal to the curve parametrically represented by x=t^(2)+3t-8 and y=2t^(2)-2t-5 at the point P(2,-1) is

Find the equation of tangent and normal to the curve x=(2a t^2)/((1+t^2)),y=(2a t^3)/((1+t^2)) at the point for which t=1/2dot

If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)) then (dy)/(dx) at t=2 ………….