Question

prove that in general a straight line cuts a conic in two points real or imaginary ​

Answer 1

Step-by-step explanation:

A

Conic Sections

The ellipse, hyperbola, and parabola (and also the circle, which is a special case of the

ellipse) are called the conic section curves (or the conic sections or just conics), since

they can be obtained by cutting a cone with a plane (i.e., they are the intersections of

a cone and a plane).

The conics are easy to calculate and to display, so they are commonly used in

applications where they can approximate the shape of other, more complex, geometric

figures. Many natural motions occur along an ellipse, parabola, or hyperbola, making

these curves especially useful. Planets move in ellipses; many comets move along a

hyperbola (as do many colliding charged particles); objects thrown in a gravitational

field follow a parabolic path.

There are several ways to define and represent these curves and this section uses

a simple geometric definition that leads naturally to the parametric and the implicit

representations of the conics.

(a)

F

F

Answer 2

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

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