A circle of radius r is concentric with an ellipse x ^ 2 a ^ 2 + y ^ 2 ~b ^ 2 =1 . If…
Mathematics · JEE Main · NTA Exams — Co-ordinate Geometry
A circle of radius r is concentric with an ellipse
\(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1 .\) If common tangent is inclined to the
major axis at an angle of\(\theta,\) then\(\tan ^{2} \theta\) equals-
\(\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1 .\) If common tangent is inclined to the
major axis at an angle of\(\theta,\) then\(\tan ^{2} \theta\) equals-
- \(\frac{r^{2}-b^{2}}{a^{2}-b^{2}}\)
- \(\frac{r^{2}-b^{2}}{a^{2}-r^{2}}\)
- \(\frac{r^{2}-b^{2}}{r^{2}-a^{2}}\)
- \(\frac{\mathrm{r}^{2}-\mathrm{a}^{2}}{\mathrm{~b}^{2}-\mathrm{r}^{2}}\)
Answer
(B) r^ 2 -b^ 2 a^ 2 -r^ 2
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