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Standard XII

Mathematics

Major Axis of Ellipse

The ends of m...

Question

The ends of major axis of an ellipse are $(5, 0) (- 5, 0)$ and one of the foci lies on $3 x - 5 y - 9 = 0$ , then the eccentricity of the ellipse is

\frac{2}{3}

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\frac{3}{5}

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\frac{4}{5}

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\frac{1}{3}

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Solution

The correct option is D $\frac{3}{5}$
Foci is point of intersection of
$3 x - 5 y - 9 = 0$ and $y = 0$
$\Rightarrow x = 3$
Distance between $(5, 0)$ and $(3, 0)$ is $a (1 - e)$
$∴ a (1 - e) = 2$
$5 (1 - e) = 2$
$1 - e = \frac{2}{5}$
$e = \frac{3}{5}$

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Similar questions

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

e = \frac{1}{2}

and foci

(\pm 2, 0)

(ii) eccentricity

e = \frac{2}{3}

snd length of latus-rectum=5
(iii) eccentricity

e = \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

(\pm 5, 0)

, foci

(\pm 4, 0)

(vii) Vertices

(0, \pm 13)

, foci

(0, \pm 5)

(viii) Vertices

(\pm 6, 0)

, foci

(\pm 4, 0)

(ix) Ends of major axis

(\pm 3, 0)

, ends of minor axis

(0, \pm 2)

(x) Ends of major axis

(0, \pm \sqrt{5})

, ends of minor axis

(\pm 1, 0)

(xi) Length of major axis 26, foci

(\pm 5, 0)

(xii) Length of minor axis 16, foci

(0, \pm 6)

(xiii) Foci

(\pm 3, 0)

, a=4

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
(iii) eccentricity e =

\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)
(xi) Length of major axis 26, foci (± 5, 0)
(xii) Length of minor axis 16 foci (0, ± 6)
(xiii) Foci (± 3, 0), a = 4

Q. The eccentricity of the ellipse, whose end points of major axis and minor axis are

(\pm \sqrt{5}, 0)

and

(0, \pm 1)

respectively, is

Q. An ellipse with its minor and major axis parallel to the coordinate axes passes through

(0, 0), (1, 0)

and

(0, 2)

. One of its foci lies on the y-axis. The eccentricity of the ellipse is?

Q. Area of the quadrilateral formed by the ends of major axis and minor axis of an ellipse is

8 \sqrt{3}

. The distance between the foci is

4 \sqrt{2}

, then the eccentricity of the ellipse is:

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The ends of major axis of an ellipse are (5,0)(−5,0) and one of the foci lies on 3x−5y−9=0, then the eccentricity of the ellipse is

The correct option is D 35 Foci is point of intersection of3x−5y−9=0 and y=0⇒x=3Distance between (5,0) and (3,0) is a(1−e)∴a(1−e)=25(1−e)=21−e=25e=35

The ends of major axis of an ellipse are $(5, 0) (- 5, 0)$ and one of the foci lies on $3 x - 5 y - 9 = 0$ , then the eccentricity of the ellipse is

The correct option is D $\frac{3}{5}$
Foci is point of intersection of
$3 x - 5 y - 9 = 0$ and $y = 0$
$\Rightarrow x = 3$
Distance between $(5, 0)$ and $(3, 0)$ is $a (1 - e)$
$∴ a (1 - e) = 2$
$5 (1 - e) = 2$
$1 - e = \frac{2}{5}$
$e = \frac{3}{5}$