Introduction to ellipse parabola hyperbola
The equation like Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 represents either a (non–degenerate) conic or a degenerate conic.
If it is a conic, then it is
a parabola if B2 - 4AC = 0.
an ellipse if B2 - 4AC < 0
a hyperbola if B2 - 4AC > 0.
Introduction to Ellipse Hyperbola Parabola
Ellipse:
An ellipse is a conic obtained on slicing across obliquely one nappe of a cone.If P is any point on the ellipse and
F1and F2 its foci, the angle subtended by F1P and F2P with the tangent at P are equal and if a source of light or sound is
placed at one focus of an ellipsoidal reflector (surface generated by revolving an ellipse about its major axis) all the
waves will be reflected so as to pass through the other focus
Hyperbola:
A hyperbola is a conic obtained on slicing a double napped cone by a plane parallel to the axis of the cone. The lines from the foci to any point of a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other.
Parabola:
A parabola is generally defined as the conic section obtained by the operation on slicing a right circular cone by a plane parallel to the line joining vertex and any other point of the cone.Between, if you have problem on these topics Formula for Volume of a Trapezoidal Prism, please browse expert math related websites for more help on 12th cbse sample papers.
If P is any point on the parabola with focus F and vertex V, the angles subtended by FP and PX with the tangent at P are equal where PX is parallel to the axis VFA of the parabola.
Problems Based on Ellipse Hyperbola Parabola
If e < 1, then the conic is an ellipse. From the figure 1we observe that F2Pi is always less than PiMi.
i.e., F2Pi / PiMi = e < 1, (i = 1, 2, 3…)
If e = 1, then the conic is a parabola. From the figure 2 we observe that FPi is always equal to PiMi.
i.e., FPi / PiMi = e = 1, (i = 1, 2, 3…)
If e > 1, then the conic is a hyperbola. From the figure 3 we observe that F1Pi is always greater than PiMi.
i.e., F1Pi / PiMi = e > 1, (i = 1, 2, 3…)
The equation like Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 represents either a (non–degenerate) conic or a degenerate conic.
If it is a conic, then it is
a parabola if B2 - 4AC = 0.
an ellipse if B2 - 4AC < 0
a hyperbola if B2 - 4AC > 0.
Introduction to Ellipse Hyperbola Parabola
Ellipse:
An ellipse is a conic obtained on slicing across obliquely one nappe of a cone.If P is any point on the ellipse and
F1and F2 its foci, the angle subtended by F1P and F2P with the tangent at P are equal and if a source of light or sound is
placed at one focus of an ellipsoidal reflector (surface generated by revolving an ellipse about its major axis) all the
waves will be reflected so as to pass through the other focus
Hyperbola:
A hyperbola is a conic obtained on slicing a double napped cone by a plane parallel to the axis of the cone. The lines from the foci to any point of a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other.
Parabola:
A parabola is generally defined as the conic section obtained by the operation on slicing a right circular cone by a plane parallel to the line joining vertex and any other point of the cone.Between, if you have problem on these topics Formula for Volume of a Trapezoidal Prism, please browse expert math related websites for more help on 12th cbse sample papers.
If P is any point on the parabola with focus F and vertex V, the angles subtended by FP and PX with the tangent at P are equal where PX is parallel to the axis VFA of the parabola.
Problems Based on Ellipse Hyperbola Parabola
If e < 1, then the conic is an ellipse. From the figure 1we observe that F2Pi is always less than PiMi.
i.e., F2Pi / PiMi = e < 1, (i = 1, 2, 3…)
If e = 1, then the conic is a parabola. From the figure 2 we observe that FPi is always equal to PiMi.
i.e., FPi / PiMi = e = 1, (i = 1, 2, 3…)
If e > 1, then the conic is a hyperbola. From the figure 3 we observe that F1Pi is always greater than PiMi.
i.e., F1Pi / PiMi = e > 1, (i = 1, 2, 3…)
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