Find the length of latus rectum of hyperbola, 9x² - 25y² = 225 .

Question

Question

Answer 1

Concept:

Hyperbola:

Equation	\(\rm \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\)	\(\rm\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1\)
Equation of Transverse axis	y = 0	x = 0
Equation of Conjugate axis	x = 0	y = 0
Length of Transverse axis	2a	2a
Length of Conjugate axis	2b	2b
Vertices	(± a, 0)	(0, ± a)
Focus	(± ae, 0)	(0, ± ae)
Directrix	x = ± a/e	y = ± a/e
Centre	(0, 0)	(0, 0)
Eccentricity	\(\rm \sqrt{1+\frac{b^{2}}{a^{2}}}\)	\(\rm \sqrt{1+\frac{b^{2}}{a^{2}}}\)
Length of Latus rectum	\(\rm \frac{2b^{2}}{a}\)	\(\rm \frac{2b^{2}}{a}\)
Focal distance of the point (x, y)	ex ± a	ey ± a

Calculation:

Given hyperbolic equation, 9x2 - 25y2 = 225

⇒ \(\rm \frac{x^{2}}{25}-\frac{y^{2}}{9}= 1\)

On comparing with standard equation , a = 5 and b = 3 .

We know the , length of latus rectum

L.R = \(\rm\frac{2b^{2}}{a}\) = \(\frac{2\times9}{5}\)

L.R = \(\frac{18}{5}\) units .

The correct option is 2.

Download Solution PDF