Find the equation of the parabola whose vertex is at the origin, axis is along the X-axis and the length of the latus rectum is 4 units.

Find the equation of the parabola with vertex at (0,0) and focus at (0,2).

A parabola has it vertex at the origin, axis along the X-axis and it passes through the point (4, -8). Find its equation.

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

Find the equation of a circle whose centre is the origin and passes through the point (2,-4).

Write the coordinates of the vertex and the focus, the equations of the directrix and the axis, and the length of the latus rectum of the parabola: (i) y ^2 = 16x

Find the equation of the straight line which cuts the Y-axis at the point (0, -2) making an angle of 30^@ with OX.

Find the equation of the ellipse referred to its centre as the origin and major axis as the X-axis give that (iii) major axis is of length 26 and foci are ( != 12, 0)

Find the equation of the circle whose centre is (2, 3) and which touches the line 3x - 4y - 1 = 0.

For the parabola y^2=20x write down the co-ordinates of the focus,length of the latus rectum.