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If \mathrm{\frac{x}{a}+\frac{y}{b}=1} touches the circle  \mathrm{x^{2}+y^{2}=r^{2}}, then prove that the point \mathrm{\left(\frac{1}{a}, \frac{1}{b}\right)} lies.

Option: 1

on a circle


Option: 2

in a circle


Option: 3

on a straight line


Option: 4

none of these.


Answers (1)

\mathrm{\frac{x}{a}+\frac{y}{b}=1} touches \mathrm{x^{2}+y^{2}=r^{2}}

\mathrm{\Rightarrow \frac{1}{\sqrt{\frac{1}{a^{2}}+\frac{1}{b^{2}}}}=r\; \Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}= \frac{1}{r^{2}}}
\mathrm{\Rightarrow\left(\frac{1}{a}, \frac{1}{b}\right)}  lies on  \mathrm{x^{2}+y^{2}=\frac{1}{r^{2}}}, which is a circle.

Hence (A) is the correct answer.

Posted by

Sumit Saini

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