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Standard XII

Mathematics

Vertical Ellipse and Terms Related to it

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Question

Label the appropriate coordinates of the ends of major and minor axis of a vertical ellipse.

(a, 0)

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(0, b)

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(- a, 0)

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(0, - b)

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Solution

\N

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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 (± 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

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

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. What are the coordinates of the foci for a vertical ellipse whose length of major axis is

2 b

and length of minor axis is

2 a

Q. 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

\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1

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