parabola

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Parts of a parabola

Two panels showing function graphing concepts: Panel A illustrates plotting an arbitrary function f by selecting values of t and marking corresponding f(t) points; Panel B graphs the specific parabola f(t) equals t squared, with plotted points showing how t values map to t squared. Both graphs use dashed lines to connect points to the axes for clarity.

Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.

Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated.

A diagram of a double cone intersected by two green planes labeled PP (picture plane) and RP (reality plane), illustrating projected conic sections in projective geometry, with the apex and a point Omega marked.

Illustration showing how a parabolic satellite dish antenna focuses incoming transmission signals onto a single point, with red lines representing signal paths reflecting off the dish surface toward the feedhorn. Insets provide a side view and a three-quarter view, highlighting the role of the paraboloid shape in signal reception.

Archimedes' parabolic segment calculation

Diagram showing the elements of a bullet's parabolic trajectory in ballistics, with a rifle at the left, labeled lines for line of sight, line of departure, and the curved bullet trajectory passing through mid-range height and hitting a target at 200 yards.

Two graphs compare projectile motion. Panel A shows a parabolic path starting high on the Z axis and curving downward to the X axis. Panel B shows a parabolic path starting at the origin, rising upward, then curving back down to the X axis, illustrating an initial upward velocity.

Figure 7: Parabola (see text).

parabola: Media

mathematics

Images

Parts of a parabola

Parts of a parabola

Parts of a parabola. The curve is symmetric about the vertical axis (axis of symmetry)....

© Watthana Tirahimonch/stock.adobe.com

Two panels showing function graphing concepts: Panel A illustrates plotting an arbitrary function f by selecting values of t and marking corresponding f(t) points; Panel B graphs the specific parabola f(t) equals t squared, with plotted points showing how t values map to t squared. Both graphs use dashed lines to connect points to the axes for clarity.

graph of a function

Part A illustrates the general idea of graphing any function: choose a value...

Encyclopædia Britannica, Inc.

Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.

Eccentricity of conic sectionsThe...

Encyclopædia Britannica, Inc.

Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated.

conic sections

The conic sections result from intersecting a plane with a double cone, as shown...

Encyclopædia Britannica, Inc.

A diagram of a double cone intersected by two green planes labeled PP (picture plane) and RP (reality plane), illustrating projected conic sections in projective geometry, with the apex and a point Omega marked.

Projective conic sectionsThe conic...

Encyclopædia Britannica, Inc.

Illustration showing how a parabolic satellite dish antenna focuses incoming transmission signals onto a single point, with red lines representing signal paths reflecting off the dish surface toward the feedhorn. Insets provide a side view and a three-quarter view, highlighting the role of the paraboloid shape in signal reception.

A paraboloid reflector

Illustration of a paraboloid focusing parallel rays, as used in satellite dish antennas...

Encyclopædia Britannica, Inc.

Archimedes' parabolic segment calculation

Archimedes' parabolic segment calculation

Employing Eudoxus's method of exhaustion, Archimedes first showed how to calculate...

Encyclopædia Britannica, Inc.

Diagram showing the elements of a bullet's parabolic trajectory in ballistics, with a rifle at the left, labeled lines for line of sight, line of departure, and the curved bullet trajectory passing through mid-range height and hitting a target at 200 yards.

Trajectory of a projectile

The parabolic trajectory of a projectile, as observed in ballistics.

Encyclopædia Britannica, Inc.

Two graphs compare projectile motion. Panel A shows a parabolic path starting high on the Z axis and curving downward to the X axis. Panel B shows a parabolic path starting at the origin, rising upward, then curving back down to the X axis, illustrating an initial upward velocity.

path of projectile

Figure 5: (A) The parabolic path of a projectile. (B) The parabolic path of a projectile...

Encyclopædia Britannica, Inc.

Figure 7: Parabola (see text).

Figure 7: Parabola (see text).

Encyclopædia Britannica, Inc.

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