Concepts of Conics and Parametric Equations

Concepts of Conics and Parametric Equations:

Chapter Summary:

Conics:

The conics get their name from the fact that they can be made by passing a plane via a double-napped cone. There are mainly four conic sections, and three degenerate cases, though, in this class we are going to look at five degenerate cases which can be formed from the general second degree equation.

The general form of second degree equation is given by the Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

Parabola:

The parabola is ‘the set of all points in a plane equidistant from a fixed point (that is, focus) and a fixed line (or directrix)’.

The distances to any point (x, y) on parabola from the focus (0, p) and the directrix y = -p, are equal to one other. This can be employed to develop the equation of the parabola.

Circle:

The circle is ‘the set of all points in a plane equidistant from the fixed point (that is, center)’.

The standard form for a circle, with center at origin is x2 + y2 = r2, here r is the radius of the circle.

Ellipse:

The ellipse is ‘the set of all points in a plane in such a way that the sum of distances from the two fixed points (that is, foci) is constant’.

The sum of distances to any point on the ellipse (x, y) from the two foci (c,0) and (-c,0) is constant. That constant will be equal to 2a.

When we let d1 and d2 bet the distances from foci to the point, then d1 + d2 = 2a.

Key Topics included in this chapter are as follows:

a) Conics
b) Translations of Conics
c) Parametric Equations

Latest technology based Algebra Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Algebra help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Algebra, project ideas and tutorials. We provide email based Algebra help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Algebra. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Algebra Homework help and assignment help services. They use their experience, as they have solved thousands of the Algebra assignments, which may help you to solve your complex issues of Algebra. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.