Conic Sections Question 156
Question: The equation of the tangents drawn at the ends of the major axis of the ellipse $ 9x^{2}+5y^{2}-30y=0 $ , are
[MP PET 1999]
Options:
A) $ y=\pm 3 $
B) $ x=\pm \sqrt{5} $
C) $ y=0,\ y=6 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Change the equation $ 9x^{2}+5y^{2}-30y=0 $ in standard form $ 9x^{2}+5(y^{2}-6y)=0 $
therefore $ 9x^{2}+5(y^{2}-6y+9)=45 $
therefore $ \frac{x^{2}}{5}+\frac{{{(y-3)}^{2}}}{9}=1 $
$ \because a^{2}<b^{2}, $ so axis of ellipse on y-axis. At y axis, put $ x=0 $ , so we can obtained vertex. Then $ 0+5y^{2}-30y=0 $
therefore $ y=0,y=6 $
Therefore, tangents of vertex $ y=0,y=6 $ .
BETA
