Application of DerivativeHard
Question
If P is a point on the curve 5x2 + 3xy + y2 = 2 and O is the origin, then OP has
Options
A.minimum value 
B.minimum value 
C.maximum value
D.maximum value 2
Solution
x = r cos θ, y = r sin θ
⇒
= 5 (1 + cos 2θ) + 3 sin 2θ + 1 - cos 2θ
= 6 + 4 cos 2θ + 3 sin 2θ, which has maximum 11 and minimum 1
∴ OP has minimum
and maximum 2.
⇒
= 5 (1 + cos 2θ) + 3 sin 2θ + 1 - cos 2θ= 6 + 4 cos 2θ + 3 sin 2θ, which has maximum 11 and minimum 1
∴ OP has minimum
and maximum 2.Create a free account to view solution
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