InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A normal to the hyperbola `(x^2)/4-(y^2)/1=1`has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`, then `a^2+b^2`is equal to5 (b)25 (c) 16(d) none of theseA. 5B. 25C. 16D. none of these |
|
Answer» Correct Answer - D The equation of the normal to the hyperbola `(x^(2))/(4)-(y^(2))/(1)=1` at `(2 sec theta, tan theta)` is `2x cos theta+y cot theta=5`. The slope of the normal is `-2 sin theta=-1` `"or "sin theta=(1)/(2)or theta=(pi)/(6)` Y-intercept of the normal `=(5)/(cot theta)=(5)/(sqrt3)` As it touches the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` As it touches the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` we have `a^(2)+b^(2)=(25)/(3)` |
|