A curve is represented parametrically by the equations `x=t+e^(at) and y=-t +e^(at, t in R and a gt 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 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

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

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 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=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

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

If a curve is represented parametrically by the equations x=4t^(3)+3 and y=4+3t^(4) and (d^(2)x)/(dy^(2))/((dx)/(dy))^(n) is constant then the value of n, is

A curve is defined parametrically be equations x=t^2a n dy=t^3 . A variable pair of perpendicular lines through the origin O meet the curve of Pa n dQ . If the locus of the point of intersection of the tangents at Pa n dQ is a y^2=b x-1, then the value of (a+b) is____

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