Conic Sections

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

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

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

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.

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

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.

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 where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

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.

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 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)