Equation nbsp- of the ellipse with foci -0- and e - 1-4 is -

The correct option is B S = (±√(2),0), e =1/4 C = (0,0), b^2 = 32(15/16) = 30 ae = √(2) a = 4√(2), x^2/32+y^2/30 = 1 ...

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Byju's Answer

Standard XII

Mathematics

Eccentricity of Ellipse

Equation nb...

Question

Equation of the ellipse with foci ( $\pm, 0$ ) and e = $\frac{1}{4}$ is

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Solution

The correct option is D

S = ( $\pm \sqrt{2}, 0$ ), e = $\frac{1}{4}$

C = (0,0), $b^{2}$ = $32 (\frac{15}{16})$ = 30

ae = $\sqrt{2}$

a = $4 \sqrt{2}$ ,
$\frac{x^{2}}{32} + \frac{y^{2}}{30}$ = 1

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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

Equation of the ellipse with foci ( $\pm, 0$ ) and e = $\frac{1}{4}$ is

Q. Find the equation of the ellipse whose foci are

(4, 0)

and

(- 4, 0),

eccentricity

e = \frac{1}{3}

Find the equation of the ellipse whose foci are at $(0, \pm 4)$ and $e = \frac{4}{5} .$

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Equation of the ellipse with foci (±,0) and e = 14 is

The correct option is D S = (±√2,0), e =14 C = (0,0), b2 = 32(1516) = 30 ae = √2 a = 4√2, x232+y230 = 1

Equation of the ellipse with foci ( $\pm, 0$ ) and e = $\frac{1}{4}$ is

The correct option is D

S = ( $\pm \sqrt{2}, 0$ ), e = $\frac{1}{4}$

C = (0,0), $b^{2}$ = $32 (\frac{15}{16})$ = 30

ae = $\sqrt{2}$

a = $4 \sqrt{2}$ ,
$\frac{x^{2}}{32} + \frac{y^{2}}{30}$ = 1