CONIC SECTIONSCan someone give me tips on doing equations about COnic SEctions the circle, parabola, hyperbola, and ellipse...... please give me some tips on formulas tnx....

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

A conic represents the intersection of a plane with a cone. The conic could be described as the locus of the points that move in a plane of a fixed point (focus), with a fixed line (directrix).

The standard conics are: circle, ellipse, hyperbola, parabola.

The standard equation of the circle is:

x^2 + y^2 = r^2

r is the radius of the circle, whose center is the origin O(0,0).

The standard equation of the ellipse is:

x^2/a^2 + y^2/b^2 = 1

a and b are the lengths of the semi-minor and semi-major axis.

The standard equation of the hyperbola is:

x^2/a^2 - y^2/b^2 = 1

a and b are the lengths of the semi-minor and semi-major axis.

Any of the conics above could be represented by the general equation:

Ax^2 + Bxy + Cy^2 + Dx + Ey  + F = 0

If we'll analyze the sign of the discriminant delta, we'll establish the type of the conic:

B^2 - 4AC = DELTA

DELTA < 0 => ellipse, circle, point

DELTA = 0 => parabola (or 2 parallel lines)

DELTA > 0 => hyperbola (2 intercepting lines)