help@askiitians.com

1800-150-456-789

Analytical Geometry> conics...

question mark

hey how to find eccentric angles at the end points of latus rectum of the ellipse x sq by 4 PLUS y sq = 1 ?

mayur g s , 13 Years ago

Grade 12th Pass

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans: 30

Sol:

Ellipse:

$\frac{x^{2}}{4}+y^{2}=1$

Let the end of the latus rectum on the ellipse be P & Q. Then

$P(acos\theta , bsin\theta )$

$Q(acos\theta , -bsin\theta )$

Since latus rectum passes through focus, we have

$acos\theta =ae$

$cos\theta =e$

$e^{2} = 1 - \frac{b^{2}}{a^{2}} = 1- \frac{1}{4} = \frac{3}{4}$

$e= \frac{\sqrt{3}}{2}$

$cos\theta = \frac{\sqrt{3}}{2}$

$\theta = cos^{-1}\frac{\sqrt{3}}{2}$

$\theta = 30$

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

Provide a better Answer & Earn Cool Goodies

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

analytical geometry

0 Answer Available

Last Activity: 2 Years ago

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

analytical geometry

0 Answer Available

Last Activity: 2 Years ago

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

analytical geometry

0 Answer Available

Last Activity: 2 Years ago

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.

analytical geometry

0 Answer Available

Last Activity: 3 Years ago

Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d

analytical geometry

0 Answer Available

Last Activity: 3 Years ago

View all Questions