Question

Through any point in the plane of a given conic there can he drawn two conics confocal with it;

Answer 1

A conic is the locus of a point whose distance from a fixed point bears a constant ratio to its distance from a fixed line. The fixed point is the focus S and the fixed line is directrix l.



The constant ratio is called the eccentricity denoted by e.

If 0 < e < 1, conic is an ellipse.
e = 1, conic is a parabola.
e > 1, conic is a hyperbola.
If fixed point of curve is (x1, y1) and fixed line is ax + by + c = then equation of the conic is
(a²+ b²) [(x — x1)² + (y — y1)²] = e²(ax + by + c)²


GENERAL EQUATION OF CONIC

A second degree equation ax2 + 2hxy + by2 + 2gx + 2fy + c= 0 represents

1) Pair of straight lines, if
Circle, if a = b, h = 0




2) Parabola, if h2 = ab and Δ ≠ 0
3) Ellipse, if h2 < ab and Δ ≠ 0
4) Hyperbola, if h2 > ab and Δ ≠ 0
5) Rectangular hyperbola, if a + b = 0 and Δ ≠ 0