Question

172 Conic Sections
The latus rectum of the ellipse 5x2 +9y2 = 45 is​

Answer 1

Answer:

50/9

Step-by-step explanation:

5x²+9y²=45

$\frac{5x^{2} }{45} +\frac{9y^{2} }{45} =1$

$\frac{x^{2} }{9} +\frac{y^{2} }{5} =1$

This is the standard form of an ellipse

So here a=9 ;b=5

The length of the latus rectum is $\frac{2b^{2} }{a}$ (a>b)

Here,

2 x 5²/9=2x25/9= 50/9