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  • If     be two foci of the ellipse, and  <img alt="\mathrm{P

If   \mathrm{F_1, F_2}  be two foci of the ellipse, and  \mathrm{P T \text { and } P N} be the tangent and normal respectively to the ellipse at point  \mathrm{P} . Then

Option: 1

\mathrm{P N \text { bisects } \angle F_1 P F_2}


Option: 2

\mathrm{P T \text { bisects } \angle F_1 P F_2}


Option: 3

\mathrm{P T \text { bisects angle }\left(180^{\circ}-\angle F_1 P F_2\right)}


Option: 4

none of these


Answers (1)

 If \mathrm{P N} bisects \mathrm{\angle F_1 P F_2} , then in \mathrm{\Delta P F_1 F_2}

\mathrm{\frac{P F_1}{P F_2}=\frac{F_1 N}{F_2 N}}                  

(Which we can prove)

Now we can say \mathrm{PN} is angle bisector of 

lines \mathrm{P F_1} and  \mathrm{P F_2} and \mathrm{P T} is \mathrm{\perp \text { to } P N}  so it

is another bisector of  \mathrm{P F_1} and \mathrm{P F_2} .

Posted by

Sumit Saini

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