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

A curve is represented paramtrically by the equations x=e^(t)cost and y=e^(t)sint where t is a parameter. Then The value of (d^(2)y)/(dx^(2)) at the point where t=0 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 the parameter.t' and the angle a between the tangent to the given curve andthe x-axis is given by,t' equals

Consider the curve represented parametrically by the equation x=t^(3)-4t^(2)-3t and y=2t^(2)+3t-5 where t in R. If H denotes the number of point on the curve where the tangent is horizontal and V the number of point where the tangent is vertical then

A curve is represented parametrically by the equations x=f(t)=a^(In(b^t))and y=g(t)=b^(-In(a^(t)))a,bgt0 and a ne 1, b ne 1" Where "t in R. The value of (d^(2)y)/(dx^(2)) at the point where f(t)=g(t) is

In the curve represented parametrically by the equations x=2log cot t+1 and y=tan t+cot t, A.tangent and normal intersect at the point (2,1) B.normal at t=(pi)/(4) is parallel to the y-axis.C.tangent at t=(pi)/(4) is parallel to the line y=x D.tangent at t=(pi)/(4) is parallel to the x-axis.

For the curve y=x e^x , the point

At any two points of the curve represented parametrically by x=a(2cos t-cos2t);y=a(2sin t-sin2t) the tangents are parallel to the axis of x corresponding to the values of the parameter t differing from each other by :