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The parametric forms are:

Circle: (r cos θ, r sin θ),

Ellipse: (a cos θ, b sin θ),

Parabola: (at^2, 2at),

Hyperbola: (a sec θ, b tan θ) or (±a cosh u, b sinh u),

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Q: Polar equation of conic section
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Related questions

The standard conic section are described today by Linear equation Bi-quadratic equations Quadratic equations Cubic equations?

The standard of conic section by linear is the second order polynomial equation. This is taught in math.


What conic section does the equation x2 4y2 6x 8y plus 1 equals 0 represent?

hyperbola


Which conic section is a closed curve?

circle and ellipse are closed curved conic section!, from bilal , Pakistan


Does a conic section have vertices?

No, a conic section does not have vertices. If it is a circle, it has a center; if it is a parabola or hyperbola, it has a focus; and if it is an ellipse, it has foci.


Who discovered the conic section?

Leibniz


What a conic section?

A conic section is a curve formed by the intersection of a plane with a cone (conical surface). If the section is parallel to the base of the cone, the conic section has a fixed diameter and is a circle. Any other plane that does not intersect the apex is either a parabola, a hyperbola, or an ellipse.


What is a conic section?

A conic section is a curve formed by the intersection of a plane with a cone (conical surface). If the section is parallel to the base of the cone, the conic section has a fixed diameter and is a circle. Any other plane that does not intersect the apex is either a parabola, a hyperbola, or an ellipse.


What is the name of a tapered cylinder with different diameters each end?

Bi-truncated conic section, or doubly-truncated conic section


Which conic section has a directrix?

Parabolas have directori.


Why does conic projection make a better map for the polar regions?

Conic projections are better for polar regions because they show these areas with less distortion compared to other map projections. Conic projections maintain shape and direction well along the lines of latitude, making them ideal for representing polar regions accurately.


Which shape never have parallel sides?

Any conic section.


How conics generated?

A conic section is generated by the intersection of a plane with a double cone. The specific shape of the conic section (ellipse, parabola, hyperbola, or circle) depends on the angle of the plane in relation to the axis of the cone. The different conic sections result from different orientations of the cutting plane.