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  • The tangents drawn from the origin to the circle <img alt="\mathrm{x^2+y^2-2 r x-2 h y+h^2=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2-2%20r%20x-2%20h%

The tangents drawn from the origin to the circle \mathrm{x^2+y^2-2 r x-2 h y+h^2=0} are perpendicular then which one is wrong
 

Option: 1

\mathrm{ h=r}


Option: 2

\mathrm {h=-r}


Option: 3

\mathrm{ r^2+h^2=1}


Option: 4

\mathrm{r^2=h^2}


Answers (1)

best_answer

The combined equation of the tangents drawn from (0,0) to \mathrm{ x^2+y^2-2 r x-2 h y+h^2=0} is

\mathrm{\left(x^2+y^2-2 r x-2 h y+h^2\right) h^2=\left(-r x-h y+h^2\right)^2 }

This equation represents a pair of perpendicular straight lines

\begin{aligned} & \therefore \text { coefficient of } x^2+\text { coefficient of } \mathrm{y}^2=0 \Rightarrow\left(h^2-r^2\right)+h^2-h^2=0 \\ & \Rightarrow \quad r^2=h^2 \Rightarrow r= \pm h . \end{aligned}

 

Posted by

Gaurav

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