The eccentricity of an ellipse is -3-2- its length of latus rectum is equal to-

The correct option is A 14 (Length of major axis)Length of latus rectum =2b^2a= 2 a ^ 2 ( 1 e ^ 2 ) #160;/ a =2a( 1 e ^ 2 ) =2a( 1 3 / 4 # ...

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Standard XII

Mathematics

Major Axis of Ellipse

The eccentric...

Question

The eccentricity of an ellipse is $\frac{\sqrt{3}}{2}$ , its length of latus rectum is equal to:

\frac{1}{2}

(Length of major axis)

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\frac{1}{3}

(Length of major axis)

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\frac{1}{4}

(Length of major axis)

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\frac{2}{3}

(Length of major axis)

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Solution

The correct option is A $\frac{1}{4}$ (Length of major axis)
Length of latus rectum $= \frac{2 b^{2}}{a} = \frac{2 a^{2} (1 - e^{2})}{a} = 2 a (1 - e^{2}) = 2 a (1 - \frac{3}{4}) = \frac{a}{2}$
Ans: C

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=

half of major axis.

Q. The length of the latus rectum of an ellipse is one third of the major axis, its eccentricity would be

Q. Find the equation of the ellipse in the following cases:
(i) eccentricity e =

\frac{1}{2}

and foci (± 2, 0)
(ii) eccentricity e =

\frac{2}{3}

and length of latus rectum = 5
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\frac{1}{2}

and semi-major axis = 4
(iv) eccentricity e =

\frac{1}{2}

and major axis = 12
(v) The ellipse passes through (1, 4) and (−6, 1).
(vi) Vertices (± 5, 0), foci (± 4, 0)
(vii) Vertices (0, ± 13), foci (0, ± 5)
(viii) Vertices (± 6, 0), foci (± 4, 0)
(ix) Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)
(x) Ends of major axis (0, ±

\sqrt{5}

), ends of minor axis (± 1, 0)
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(xii) Length of minor axis 16 foci (0, ± 6)
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Q. Find the length of major axis, minor axis, latus rectum and eccentricity of the ellipse

9 x^{2} + 16 y^{2} = 144

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

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The eccentricity of an ellipse is √32, its length of latus rectum is equal to:

The correct option is A 14 (Length of major axis)Length of latus rectum =2b2a=2a2(1−e2)a=2a(1−e2)=2a(1−34)=a2Ans: C

The eccentricity of an ellipse is $\frac{\sqrt{3}}{2}$ , its length of latus rectum is equal to:

The correct option is A $\frac{1}{4}$ (Length of major axis)
Length of latus rectum $= \frac{2 b^{2}}{a} = \frac{2 a^{2} (1 - e^{2})}{a} = 2 a (1 - e^{2}) = 2 a (1 - \frac{3}{4}) = \frac{a}{2}$
Ans: C