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From a point ‘A’ on the circle \mathrm{x^2+y^2=r^2} tangents AB and AC are drawn to the ellipse \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}=1}, where r > a > b and B, C lies on the ellipse, D is any point on the circumcircle of triangle ABC such that ABDC is a parallelogram, then

 

Option: 1

\mathrm{(a+b)^2=r^2}


Option: 2

\mathrm{a^2+b^2=r^2


Option: 3

\mathrm{a^2+b^2=2r^2}


Option: 4

none of these 

 


Answers (1)

best_answer

\mathrm{\text { Clearly } \angle \mathrm{BAC}=\frac{\pi}{2}}

Thus ‘A’ should lie on the director circle of the ellipse 

\mathrm{\begin{aligned} & \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ & \Rightarrow \mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2+\mathrm{b}^2 \text { and } \mathrm{x}^2+\mathrm{y}^2=\mathrm{r}^2 \end{aligned}} are both indentical 

\mathrm{\Rightarrow r^2=a^2+b^2}

 

 

Posted by

shivangi.bhatnagar

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