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

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

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 circle whose radius 4 and which is concentric with the circle x ^2 + y ^2 + 2x - 6y = 0.

Find the equation of the tanget to the parabola (i) y^2 = 4x which is parllel to 2x + y + 3 = 0

Find the differential equation of all parabolas : y^2 = 4ax

Find the equation of the straight line which is parallel to 2x-y+3=0 and passes through the point (2,9).

Find the equation of the tangent and normal to the following curve at the given point : x^2/a^2-y^2/b^2=1 at (x_0,y_0)