`t in R` parametric equation of parabola are `x=at^2 and y = 2at `.

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 alpha between the tangent to the given curve andthe x-axis is given by, 't' equals

Find the area of the region bounded by the parabola y = x^(2) and y = |x|.

Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parametric equations of the line intersection of the given planes are x=3+14 t ,y=2t ,z=15 tdot Statement 2: The vector 14 hat i+2 hat j+15 hat k is parallel to the line of intersection of the given planes.

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

AA t in R, …….is the point lies on parabola x^(2) = 4ay .

Let V be the vertex and L be the latusrectum of the parabola x^2=2y+4x-4 . Then the equation of the parabola whose vertex is at V. Latusrectum L//2 and axis s perpendicular to the axis of the given parabola.

Find the area of the region bounded by the parabola y=x^2 and y=|x|

Find the equation of the parabola with focus (2,0) and directrix x=-2 .

Obtain lnght of latus rectum and equation of direction of the parabola (x + 1)^(2) = 4(y + 2) by shifting origin at point (-1, -2).

The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^2+t+1; t in R , is