Find the equation of the hyperbola with vertices `(+-4,0)` and foci at `(+-6,0)`.

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

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

Find the equation of the ellipse whose vertices are (0,+-6) and eccentricty is 1/3.

Find the equation of the circle whose centre is (4, 5) and which passes through the centre of the circle x ^2 + y ^2 + 4x -6y - 12 = 0

Find the area of the triangle whose vertices are (0, 0), (a, 0) and (0, b).

Find the equation of the ellipse whose foci are (3,0) and(-3,0) and eccentricity 2/3.

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

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 eccentricity of the hyperbola (i) x ^2 /4 - y ^2 = 1

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)