Conic Section Examples

Conic sections graphed by eccentricity.

Conic section examples. Find the coordinates of the focus axis the equation of the directrix and latus rectum of the parabola y 2 16x. If 0 β α then the plane intersects both nappes and conic section so formed is known. Tons of well thought out and explained examples created especially for students.

Find an equation of the circle with centre at 0 0 and radius r. The appearance of each conic section has trends based on the values of the constants in the equation. The equations of conic sections are very important because they tell you not only which conic section you should be graphing but also what the graph should look like.

Therefore the equation of the circle is x 2 y 2 r 2. If α β the conic section formed is a parabola represented by the orange curve as shown below. Introduction to conic sections by definition a conic section is a curve obtained by intersecting a cone with a plane.

Usually these constants are referred to as a b h v f and d. Circles parabolas ellipses and hyperbolas. The circle is a special case of the ellipse though historically it was sometimes called a fourth type.

Scroll down the page for more examples and solutions on conic sections. A conic section can either be a porabola an ellipse a circle or a hyperbola depending on the angle of the intersection throught the cone. This graph shows an ellipse in red with an example eccentricity value of latex 0 5 latex a parabola in green with the required eccentricity of latex 1 latex and a hyperbola in blue with an example eccentricity of latex 2 latex.

The ancient greek mathematicians studied conic sections culminating around 200. Depending on the angle of the plane relative to the cone the intersection is a circle an ellipse a hyperbola or a parabola. It also shows one of the degenerate hyperbola cases the straight.