find the equations of the latus rectum of an ellipse 9x^2+4y^2-18x-8y-23=0

Open in App

Solution

Dear Student
$9 x^{2} + 4 y - 18 x - 8 y - 23 = 0 \Rightarrow \frac{{(x - 1)}^{2}}{4} + \frac{{(y - 1)}^{2}}{9} = 1 T a k i n g o r i g i n a t (1, 1) b y s h i f t i n g a c c o r d i n g l y, w e g e t : \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1 H e r e, a = 2, b = 3 e^{2} = 1 - \frac{a^{2}}{b^{2}} = 1 - \frac{4}{9} = \frac{5}{9} e = \pm \frac{\sqrt{5}}{3} F o c u s : (0, \pm b e) = (0, \pm \sqrt{5}) E q n . o f L a t u s R e c t u m : y = \pm \sqrt{5} S h i f t i n g t h e o r i g i n b a c k t o (0, 0) i . e ., y \leftrightarrow y - 1 y - 1 = \pm \sqrt{5} \Rightarrow y = 1 \pm \sqrt{5}$
Regards

Suggest Corrections

Similar questions

9 x^{2} + 4 y^{2} - 18 x - 8 y - 23 = 0

9 x^{2} + 4^{2} - 18 x - 8 y - 23 = 0

x^{2} + 4 y^{2} + 8 y - 2 x + 1 = 0

x^{2} + 4 y^{2} + 8 y - 2 x + 1 = 0

9 x^{2} + 4 y^{2} = 1

Join BYJU'S Learning Program