CEE Kerala Engineering
CEE Kerala Engineering Solved Paper-2010
question_answer
If a point\[P(x,\text{ }y)\]moves along the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]and if C is the centre of the ellipse, then the sum of maximum and minimum values of CP is
A) 25
B) 9
C) 4
D) 5
E) 16
Correct Answer:
B
Solution :
The given equation of ellipse is \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] Comparing it with \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\Rightarrow \] \[a=5,b=4\] and centre of ellipse = (0, 0) \[\therefore \]Maximum distance of CP \[=\sqrt{{{(5-0)}^{2}}+{{(0-0)}^{2}}}=5\] and minimum distance of CP \[=\sqrt{{{(0-0)}^{2}}+{{(4-0)}^{2}}}=4\] \[\therefore \] Sum \[=5+4=9\]