What is the formula for latus rectum of hyperbola?

The Latus rectum of a hyperbola is defined as a line segment perpendicular to the transverse axis through any of the foci and whose ending point lies on the hyperbola. The length of the latus rectum of a hyperbola is 2b²/4a.

What is the length of the latus rectum of hyperbola?

2b2/a
Length of Latus Rectum of Hyperbola The ends of the latus rectum of a hyperbola are (ae, ±b2/a2), and the length of the latus rectum is 2b2/a.

How do you find the equation of a parabola given the latus rectum?

use h, k, and p to find the coordinates of the focus, (h,k+p) use k and p to find the equation of the directrix, y=k−p. use h, k, and p to find the endpoints of the latus rectum, (h±2p,k+p)

What is the length of the latus rectum of the parabola y 2 16x?

Hence, the length of latus rectum is 8.

What is the length of the latus rectum?

In a circle , the latus rectum is always the length of the diameter . In a hyperbola , it is twice the square of the length of the transverse axis divided by the length of the conjugate axis.

What is the equation of the directrix of the parabola y 2 16x?

For the standard form of the parabola y2=−4ax, the equation of the directrix is x+a=0.

How to find the length of the latus rectum of a hyperbola?

The ends of the latus rectum of a hyperbola are (ae, ±b 2 /a 2 ), and the length of the latus rectum is 2b2/a. The summary for the latus rectum of all the conic sections are given below: Find the length of the latus rectum whose parabola equation is given as, y 2 = 12x.

How do you find the equation of the hyperbola with foci?

Question 1: Find the equation of the hyperbola where foci are (0, ±12) and the length of the latus rectum is 36. Answer: The foci are (0, ±12). Hence, c = 12. Length of the latus rectum = 36 = 2b 2 /a Since ‘a’ cannot be negative, we take a = 6 and so b 2 = 36a/2 = (36 x 6)/2 = 108.

What is the length of the latus rectum of an ellipse?

Therefore, the length of the latus rectum of an ellipse is given as: = 2b 2 /a = 2 (2) 2 /3 = 2 (4)/3

How do you find the eccentricity of a hyperbola?

We take a point P at A and B as shown above. Therefore, by the definition of a hyperbola, we have Hence, BF 1 – BF 2 = BA + AF 1 – BF 2 = BA = 2a. You can download the Hyperbola Cheat Sheet by clicking on the download button below Like in the ellipse, e = c/a is the eccentricity in a hyperbola. Also, ‘c’ is always greater than or equal to ‘a’.