Find The Equation Of Pair Of Tangents Drawn From The Point (1, 2) And (2, 1) To The Ellipse .

The equation x² + 4xy + y² + 2x + 4y + 2 = 0 represents

The equation of the tangent to the ellipse x² + 16y² = 16 making an angle of 60⁰ with x-axis is

The equation of the ellipse whose foci are  and one of its directrix is 5x = 36.

Center of hyperbola 9x² – 16y² + 18x + 32y – 151 = 0 is

The equation of the ellipse whose centre is (2, –3), one of the foci is (3, –3) and the responding vertex is (4, –3) is

Find the eccentricity of the ellipse, whose foci are (–3, 4) and (3, –4) and which passes through the point (1, 2)

If  is a tangent to the ellipse , then find out the eccentric angle of the point of tangency.

For what value of λ dose the line y = x + λ touches the ellipse 9x² + 16y² = 144.

Find the equations of the tangents to the ellipse 3x² + 4y² = 12 which perpendicular to the line y + 2x = 4.

A tangent to the circle x² + y² = 5 at the point (–2, 1) intersect the ellipse  at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.