Conic Sections Question 33
The equations of the tangents to the ellipse $ 9x^{2}+16y^2=144 $ which pass through the point (2, 3) are
[MP PET 1996]
Options:
A) $ y=3,\ x+y=5 $
B) $ y=-3,\ x-y=5 $
C) $ y=4,\ x+y=3 $
D) $ y=-4,\ x-y=3 $
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Answer:
Correct Answer: A
Solution:
The tangent will be $ y-3=m(x-2) $
therefore $ y-mx=3-2m. $
But it is tangent to the given ellipse, therefore $ m=0 $ or $ m=-1 $ .
Hence tangents are $ y=3 $ and $ x+y=5 $ .
BETA
