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

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

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: 3 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: 3 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