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Maximum number of common normals of \mathrm{\mathrm{y}^{2}=4ax} and \mathrm{x^{2}=4by} can be equal to

Option: 1

3


Option: 2

4


Option: 3

6


Option: 4

5


Answers (1)

best_answer

Normals to \mathrm{y^{2}=4 a x\: and \: x^{2}=4 b y\: in \: terms\: of \: ' m ' \: are \: y=m x-2 a m-a m^{3}}

and \mathrm{y=m x+2 b+\frac{b}{m^{3}}}.

For a common normal
\mathrm{2 b+\frac{b}{m^{2}}-2 a m+a m^{3}=0}
\mathrm{\Rightarrow \quad a m^{5}+2 a m^{3}+2 b m^{2}+b=0}

That means there can be atmost 5 common normals.

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