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Q.

If $f^{11} (x) + f^{1} (x) + f^{2} (x) = x^{2}$ be the differential equation of a curve and let P be the point of maxima then number of tangents which can be drawn from P to $x^{2} - y^{2} = a^{2}$ is/are

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a

1

b

2

c

3

d

0

answer is B.

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Detailed Solution

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At point of maxima $f' (x) = 0$ and $f " (x) < 0$
$\Rightarrow f " (x) = x^{2} - f^{2} (x) \leq 0$
Since the curve is $x^{2} - y^{2} = a^{2}$ and $x^{2} - f^{2} (x) \leq 0$
${x_{1}}^{2} - {y_{1}}^{2} < a^{2}$
Point lies outside hyperbola
Hence 2 tangents

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