Conic Sections Question 88
Question: The ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ and the straight line $ y=mx+c $ intersect in real points only if
[MNR 1995]
Options:
A) $ a^{2}m^{2}<c^{2}-b^{2} $
B) $ a^{2}m^{2}>c^{2}-b^{2} $
C) $ a^{2}m^{2}\ge c^{2}-b^{2} $
D) $ c\ge b $
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Answer:
Correct Answer: C
Solution:
To cut at real points, $ c^{2}\le a^{2}m^{2}+b^{2} $
therefore $ a^{2}m^{2}\ge c^{2}-b^{2} $ .
BETA
