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

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

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).

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

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

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

An equilateral triangle is inscribed in the parabola y² = 4ax whose one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

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.

An equilateral triangle is inscribed in the parabola y² = 4ax where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

A man running a racecourse notes that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.

A rod AB of length 15 cm rests in between two coordinate axes in such a way that the end point A lies on x-axis and end point B lies on y-axis. A point P(x, y) is taken on the rod in such a way that AP = 6 cm. Show that the locus of P is an ellipse.

Convert the complex number in polar form: (-16)/(1+i√3)