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
C) On the major axis
D) On the minor axis
Show Answer
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) lies on it.
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