Conic Sections Question 504
Question: The position of the point (1, 3) with respect to the ellipse $ 4x^{2}+9y^{2}-16x-54y+61=0 $
[MP PET 1991]
Options:
A) Outside the ellipse
B) On the ellipse, the sum of the distances from any point on the ellipse to the two foci is constant.
C) On the major axis of an ellipse
D) On the minor axis of an ellipse
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Answer:
Correct Answer: C
Solution:
$ E\equiv 4+9{{(3)}^{2}}-16(1)-54(3)+61<0 $
Therefore, the point is inside the ellipse. $ \frac{4{{(x-2)}^{2}}}{36}+\frac{9{{(y-3)}^{2}}}{36}=1 $
Equation of major axis is $ y-3=0 $ and point (1, 3) does not lie on it.
BETA
