Conic Sections

Find the equation of the hyperbola whose vertices are (±6,0) and one of the directrices is x = 4.

Find the equation of the ellipse with foci at (±5,0) and x =36/5 as one of the directrices.

Find the equation of the ellipse, with major axis along the x-axis and passing through the points (4, 3) and (– 1, 4).

Given the ellipse with equation 9x² + 25y² = 225, find the major and minor axes, eccentricity, foci and vertices.

Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y +3 = 0

Find the vertex, axis, focus, and latus rectum of the parabola 4y²+12x–20y+67=0

Find the equation of the hyperbola where foci are (0,±12) and the length of the latus rectum is 36.

Find the equation of the parabola whose focus is the origin and whose directrix is the line 2x + y – 1 = 0 

Find the equation of the ellipse which passes through the point (–3, 1) and has eccentricity √2/5 with x-axis as its major axis and centre at the origin.