Equation of the ellipse with foci - 5-0 and length of major axis 26 is

The correct option is C S = ±5,0, 2a = 26 ae = 5, a =13 e = 5/13, b^2 = a^2(1 e^2) =169 (1 25/169) = 144 x^2/169+y^2/144 = 1 ...

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Byju's Answer

Standard XII

Mathematics

Major Axis of Ellipse

Equation of t...

Question

Equation of the ellipse with foci ( $\pm$ 5,0) and length of major axis 26 is

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Solution

The correct option is D

S = $\pm 5, 0$ , 2a = 26

ae = 5, a =13

e = $\frac{5}{13}$ ,
$b^{2}$ = $a^{2} (1 - e^{2})$

=169 (1 - $\frac{25}{169}$ ) = 144

$\frac{x^{2}}{169} + \frac{y^{2}}{144}$ = 1

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Similar questions

Q. Find the equation for the ellipse that satisfies the given conditions: Length of major axis

26

, foci

(\pm 5, 0) .

Find the equation for the ellipse that satisfies the given conditions,
Length of major axis 26, foci $(\pm 5, 0)$

Q. 15.Length of major axis 26, foci (+ 5, 0)

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)
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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

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Equation of the ellipse with foci (±5,0) and length of major axis 26 is

The correct option is D S = ±5,0, 2a = 26 ae = 5, a =13 e = 513, b2 = a2(1−e2) =169 (1 - 25169) = 144 x2169+y2144 = 1

Equation of the ellipse with foci ( $\pm$ 5,0) and length of major axis 26 is

The correct option is D

S = $\pm 5, 0$ , 2a = 26

ae = 5, a =13

e = $\frac{5}{13}$ ,
$b^{2}$ = $a^{2} (1 - e^{2})$

=169 (1 - $\frac{25}{169}$ ) = 144

$\frac{x^{2}}{169} + \frac{y^{2}}{144}$ = 1