What is the difference between pole and polar?

The pole of a line L in a circle C is a point P that is the inversion in C of the point Q on L that is closest to the center of the circle. Conversely, the polar line (or polar) of a point P in a circle C is the line L such that its closest point Q to the center of the circle is the inversion of P in C.

What is pole and polar in ellipse?

Polar of a point – formula Consider a point P inside or outside ellipse and a line passing through ellipse intersecting it at points Q and R . Then the locus of point of intersection of tangents at Q and R is called polar. Point P is called the pole.

What is the polar equation of a parabola?

Deriving the polar equation of a parabola with focus at the origin and directrix at y=−p. I started by saying the the standard equation of a parabola, in Cartesian form is y=x24p, where p>0 and the focus is at F(0,p) and the directrix is y=−p.

What is meant by polar of a circle?

: either of the two parallels of latitude each at a distance from a pole of the earth equal to about 23 degrees 27 minutes.

How do you find polar and Poles?

Draw any chord AB and A’B’ passing through P. If tangents to the circle at A and B meet at Q, then locus of Q is called the polar of P with respect to circle and P is called the pole and if tangents to the circle at A’ and B’ meet at Q’, then the straight line QQ’ is polar with P as its pole.

What are the poles of a polar graph?

The polar grid is represented as a series of concentric circles radiating out from the pole, or the origin of the coordinate plane. The reference point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the reference direction is the polar axis.

What is meant by conjugate lines?

1 of a conic section : two lines each of which passes through the pole of the other. 2 of a quadric : two lines so arranged that each intersects the polar line of the other.

Does it form circles at the pole?

All the meridians on Earth are great circles. All these lines of longitude meet at the poles, cutting the Earth neatly in half. The Equator is another of the Earth’s great circles. If you were to cut into the Earth right on its Equator, you’d have two equal halves: the Northern and Southern Hemispheres.

What is conjugate angle?

conjugate anglesnoun. A pair of angles that sum to 360 degrees.

Which is the pole and polar of the parabola?

Then the locus of the point of intersection of the tangents to the parabola at Q and R is called the polar of the given point P w.r.t. the parabola and the point P itself is called the pole of the polar. ), the points are said to be conjugate points.

How is the conic of a parabola determined?

Any conic may be determined by three characteristics: a single focus, a fixed line called the directrix, and the ratio of the distances of each to a point on the graph. Consider the parabolax = 2 + y2 shown in (Figure). Figure 2. In The Parabola, we learned how a parabola is defined by the focus (a fixed point) and the directrix (a fixed line).

How are pole, polar and reciprocation generalized?

General conic sections. The concepts of pole, polar and reciprocation can be generalized from circles to other conic sections which are the ellipse, hyperbola and parabola. This generalization is possible because conic sections result from a reciprocation of a circle in another circle, and the properties involved,…

How to graph a hyperbola in polar coordinates?

Graph r = 8 2 − 3 sin θ. First, we rewrite the conic in standard form by multiplying the numerator and denominator by the reciprocal of 2, which is 1 2. Because e = 3 2, e > 1, so we will graph a hyperbola with a focus at the origin.

What is the difference between pole and polar? The pole of a line L in a circle C is a point P that is the inversion in C of the point Q on L that is closest to the center of the circle. Conversely, the polar line (or polar) of a point P in a…