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  • For the parabola and the circle <img alt="\mathrm{x^{2}+y^{2}+2 b x=0

For the parabola \mathrm{y^{2}=4 a x} and the circle \mathrm{x^{2}+y^{2}+2 b x=0} to have more than one common tangents

Option: 1

\mathrm{ab}<0


Option: 2

\mathrm{ab}>0


Option: 3

\mathrm{a b<-1}


Option: 4

\mathrm{a b<-2}


Answers (1)

best_answer

Both the parabola and the circle pass through the origin. The equation of the circle may be written as

\mathrm{(x+b)^{2}+y^{2}=b^{2}}.
For more than one common tangents, the focus (a, 0) and the centre (-b, 0) must be on the opposite side of the origin.

\Rightarrow \mathrm{a}(-\mathrm{b})<0 \Rightarrow \mathrm{ab}>0
 

Posted by

manish painkra

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