Consider the ellipse x^(2)/(tan^(2)alpha...

Consider the ellipse `x^(2)/(tan^(2)alpha)+y^(2)/(sec^(2)alpha)=1` where `alphain(0,pi/2)`. Which of the following quantities would vary as `alpha` varies?

A

degree of flatness

B

ordinate of vertex

C

coordinates of foci

D

length of the latusrectum

Text Solution

Verified by Experts

The correct Answer is:

C

Topper's Solved these Questions

CONIC SECTIONS
VMC MODULES ENGLISH|Exercise LEVEL - 2|111 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise Numerical Value Type for JEE Main|15 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
DIFFERENTIAL CALCULUS
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

Similar Questions

Explore conceptually related problems

For the hyperbola x^2/ cos^2 alpha - y^2 /sin^2 alpha = 1;(0 lt alphalt pi/4) . Which of the following remains constant when alpha varies?

if (1+tan alpha )(1+tan4 alpha ) =2 where alpha in (0 , pi/16 ) then alpha equal to

If latus recturn of the ellipse x^2 tan^2 alpha+y^2 sec^2 alpha= 1 is 1/2 then alpha(0 lt alpha lt pi) is equal to

For the hyperbola (x^2)/(cos^2alpha)-(y^2)/(sin^2alpha)=1 , which of the following remains constant when alpha varies? (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci

If cos 5 alpha=cos^5 alpha, where alpha in (0,pi/2) then find the possible values of (sec^2 alpha+cosec^2 alpha+cot^2 alpha).

Solve : tan ^(2) alpha + sec alpha - 1 = 0,0 le alpha lt 2pi.

Minimum value of (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha), where alpha!=pi/2,beta!=pi/2 ,0

The value of expression (tan alpha+sin alpha)/(2"cos"^(2)(alpha)/(2)) for alpha=(pi)/(4) is :

Consider equation (x - sin alpha) (x-cos alpha) - 2 = 0 . Which of the following is /are true?

"If "y=sqrt((2(tanalpha+cotalpha))/(1+tan^(2)alpha)+(1)/(sin^(2)alpha))"when "alpha in ((3pi)/(4),pi)"then find "(dy)/(dalpha)" at" alpha=(5pi)/(6)

VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 1

The eccentricity of ellipse 4(x-2y+1)^2 +9(2x+y+2)^2=180 is
Text Solution
|
The equation, 2x^2+ 3y^2-8x-18y+35= K represents (a) no locus if k g...
Text Solution
|
Consider the ellipse x^(2)/(tan^(2)alpha)+y^(2)/(sec^(2)alpha)=1 where...
Text Solution
|
If alpha and beta are the eccentric angles of the extremities of a f...
Text Solution
|
If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2)...
Text Solution
|
The equation of the tangents to the ellipse 4x^(2)+3y^(2)=5, which are...
Text Solution
|
The equation of normal to the ellipse 4x^2 +9y^2 = 72 at point (3,2) i...
Text Solution
|
The locus of the foot of the perpendicular from the foci an any tangen...
Text Solution
|
Show that the tangents drawn at those points of the ellipse (x^(2))/(a...
Text Solution
|
Let the two foci of an ellipse be (-1, 0) and (3, 4) and the foot of p...
Text Solution
|
Let the two foci of an ellipse be (-1,0) and (3,4) and the foot of per...
Text Solution
|
Let the two foci of an ellipse be (-1,0) and (3,4) and the foot of per...
Text Solution
|
Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)...
Text Solution
|
PQ is a double ordinate of the parabola y^(2)=4ax. If the normal at P ...
Text Solution
|
The area of the rectangle formed by the perpendicular from the center ...
Text Solution
|
The length ofthe normal (terminated by the major axis) at a point of t...
Text Solution
|
Find the middle point of the chord intercepted on the line 2x-y+3 =0 b...
Text Solution
|
Find the locus of the mid point of chords of the ellipse x^(2)/a^(2)+y...
Text Solution
|
CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^...
Text Solution
|
The equation of the chord of (x^(2))/(36)+(y^(2))/(9)=1 which is ...
Text Solution
|