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Standard XII

Mathematics

Centre of Ellipse

Which of the ...

Question

Which of the following is/are not false?

The mid point of the line segment joining the foci is called the centre of the ellipse.

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The line segment through the foci of the ellipse is called the major axis.

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The end points of the major axis are called the vertices of the ellipse.

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Ellipse is symmetric with respect to Y-axis only.

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Solution

The correct options are
A The mid point of the line segment joining the foci is called the centre of the ellipse.
B The line segment through the foci of the ellipse is called the major axis.
C The end points of the major axis are called the vertices of the ellipse.
(A) Midpoint of the line segment joining the foci is called the centre of ellipse: TRUE

(B) Line segment through the foci is called major axis: TRUE

(C) End point of major axis are called vertices of ellipse: TRUE

(D) Ellipse is symmetric with respect to Y-axis only.: FALSE
(Ellipse is symmetric to both x-axis and y-axis)

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Similar questions

Q. If the angle between the lines joining the end points of minor axis of an ellipse with its foci is

\frac{π}{2}

, then the eccentricity of the ellipse is

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. Arrange the eccentricities of the following ellipses in particular order.

A- Ellipse whose Latus rectum is half of its major axis.

B- Ellipse whose distance between the foci is equal to the distance between a focus and one end of minor axis

C- Ellipse whose major axis is double the minor axis.

D- Ellipse whose distance between the foci is

6

and the length of minor axis is

8

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. Let

P

be any point on any directrix of an ellipse. Then chords of contact of point

P

with respect to the ellipse and its auxiliary circle intersect at

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