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Equation of common tangent of \mathrm{y^{2}=4 a x} and \mathrm{x^{2}=4by}  is

Option: 1

\mathrm{x+y-a=0}


Option: 2

\mathrm{x-y-a=0}


Option: 3

\mathrm{x-y+a=0}


Option: 4

\mathrm{x+y+a=0}


Answers (1)

best_answer

Let \mathrm{y=m x+\frac{a}{m}} be a tangent of \mathrm{y^{2}=4 a x}. It will touch \mathrm{x^{2}=4ay}, provided

\mathrm{x^{2}=4 a\left(m x+\frac{a}{m}\right)} has equal roots.

\mathrm{ \therefore \quad 16 a^{2} m^{2}=-16 \frac{a^{2}}{m} }
\mathrm{ \Rightarrow \quad m=-1 }.

Thus common tangent is
\mathrm{ y+x+a=0 }.

Posted by

Devendra Khairwa

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