Find the length of the common chord of the parabola `y^2=4(x+3)` and the circle `x^2+y^2+4x=0` .

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

Find the area of the region bounded by the parabolas y^2=4x and x^2=4y .

The length of the common chord of the two circles x^2+y^2-4y=0 and x^2+y^2-8x-4y+11=0 is

Find the equation of the directrix of the parabola x^2-4x-3y+10=0

Show that the common tangents to the parabola y^2=4x and the circle x^2+y^2+2x=0 form an equilateral triangle.

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

The vertex of the parabola y^2 + 4x = 0 is

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3dot