Current location - Training Enrollment Network - Mathematics courses - Eh, what does the "focal radius" in the conic section in that mathematics mean? What is the formula? Thank you for your answers!
Eh, what does the "focal radius" in the conic section in that mathematics mean? What is the formula? Thank you for your answers!
Generally speaking, the formula of focal radius and its derivation are 1. Let m(xo, y0) be an ellipse x2/a2+

y2/B2 = 1(a & gt; B>0), r 1 and r2 are the distances between point m and points f 1(-c, 0) and f2(c, 0), then (left focal length) r 1=a+ex0, (right focal length) R2 = a.

-ex0, where e is eccentricity.

Deduction: r 1/∣mn 1∣=

r2/∣mn2∣=e

Available: r 1=

e∣mn 1∣=

e(a^2/

c+x0)=

a+ex0,r2=

e∣mn2∣=

e(a^2/

c-x0)=

a-ex0 .

Similarly: ∣mf 1∣=

a+ey0,∣mf2∣=

A-ey0 .2. The focal radius formula of hyperbola The focal radius formula when point P is on the right branch of hyperbola (where f 1 is the left focus and f2 is the right focus) is derived from the second definition, where a is the real semi-axis length, e is the eccentricity and x is the eccentricity. Is the abscissa of point p. |pf2|=ex。 -

a

And only remember that the right branch, the left branch and the right branch are just a negative sign.

If the focus is on the y axis, just remember the above branch in the same way.

Radius of hyperbola passing through right focal point r = | a-ex |

The radius of hyperbola passing through the left focus is r = | a+ex | 3. Parabola Parabola's focal radius formula r=x+p/2.

Diameter: the chord of a conic curve (except a circle) passing through the focal point and perpendicular to the axis.

The path of hyperbola and ellipse is 2b 2/a, and the focal length is a 2/c-c-c.

The path of the parabola is 2p.

Parabola y 2 = 2px

(p>0), c(xo, yo) is a point on a parabola, and the focal radius |cf|=xo+p/2.