Home
Class 12
MATHS
Find the length of Latus rectum of the e...

Find the length of Latus rectum of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`.

Text Solution

Verified by Experts

The correct Answer is:
4
Let `P-=(2sqrt(3)cos theta, 2 sin theta)`
and `Q-=(2sqrt(3)cos((pi)/(2)+theta),2sin((pi)/(2)+theta))`
or `Q-=(-2sqrt(2)sin theta, 2 cos theta)`
`(PQ)^(2)=8(cos theta+sin theta)^(2)+4(sin theta-cos theta)^(2)=12+4 sin 2 theta`
`:. (PQ)_("max")=4`
Promotional Banner

Similar Questions

Explore conceptually related problems

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(4)+(y^(2))/(25)=1

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(16)+(y^(2))/(9)=1

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(25)+(y^(2))/(100)=1

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(36)+(y^(2))/(16)=1

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(49)+(y^(2))/(36)=1

In each of the Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. (x^(2))/(100)+(y^(2))/(400)=1

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse (x^(2))/(25)+(y^(2))/(9)=1

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

In each of the find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. (x^(2))/(16)-(y^(2))/(9)=1

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.