
Prove that the extremities of latus recta of all ellipses a given major axis lie in the parabola
Answer
508.5k+ views
1 likes
Hint: Here we will use a known fact that for a standard ellipse , the endpoints of latus recta are given by
where and
Complete step-by-step answer:
We know that for a standard ellipse ,
The coordinates of endpoints of the latus rectum are:
And,
……………………….(2)
Now in order to prove that major axis lie in the parabola
Now we also know that :-
………………….(3)
Putting the value of in equation 2 we get:-
Now putting the value of e from equation 1 we get:-
Simplifying it further we get:-
Now taking LCM and then simplifying it further we get:-
Now on cross multiplying we get:-
Now taking –a as common from right hand side we get:-
which is the required equation of parabola
Hence proved.
Note: The students might make the mistake of forgetting any of the coordinates of the endpoints of the latus rectum of the ellipse which may lead to failure of the proof.
Also, students should note that the following formula is applicable only if :
where
Complete step-by-step answer:
We know that for a standard ellipse
The coordinates of endpoints of the latus rectum are:
And,
Now in order to prove that major axis lie in the parabola
Now we also know that :-
Putting the value of
Now putting the value of e from equation 1 we get:-
Simplifying it further we get:-
Now taking LCM and then simplifying it further we get:-
Now on cross multiplying we get:-
Now taking –a as common from right hand side we get:-
which is the required equation of parabola
Hence proved.
Note: The students might make the mistake of forgetting any of the coordinates of the endpoints of the latus rectum of the ellipse which may lead to failure of the proof.
Also, students should note that the following formula is applicable only if
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

What is the technique used to separate the components class 11 chemistry CBSE

Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

Give two reasons to justify a Water at room temperature class 11 chemistry CBSE
