Conic Sections Question 207
Question: Consider any point P on the ellipse $ \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 $ in the first quadrant. Let r and s represent its distances from (4, 0) and (-4, 0) respectively, then (r + s) is equal to
Options:
A) 10 unit
B) 9 unit
C) 8 unit
D) 6 unit
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 $ Put $ x=3 $ $ \frac{9}{25}+\frac{y^{2}}{9}=1 $ $ y=\frac{12}{5} $ $ P=(3,12/5) $ $ r=PO=\sqrt{{{(4-3)}^{2}}+{{( 0-\frac{12}{5} )}^{2}}} $ $ =17/5 $ $ S=PO’=\sqrt{[-4-3]+{{( 0-\frac{12}{5} )}^{2}}} $ $ =33/5 $ $ r+s=\frac{17}{5}+\frac{33}{5}=\frac{50}{5}=10units $
BETA
