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^(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

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=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

Eccentricity of ellipse whose equation is x=3 (cos t + sin t), y = 4 (cos t - sin t) where t is parameter is

x=e^t (sin t + cos t ),y=e^t(sin t -cos t)

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

The equation x= t^(3) + 9 and y= (3t^(3))/(4) + 6 represents a straight line where t is a parameter. Then y- intercept of the line is :