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

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 of t...

Question

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

$\frac{x^{2}}{16} + \frac{y^{2}}{14}$ = 1

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$\frac{x^{2}}{18} + \frac{y^{2}}{16}$ = 1

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$\frac{x^{2}}{20} + \frac{y^{2}}{18}$ = 1

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$\frac{x^{2}}{32} + \frac{y^{2}}{30}$ = 1

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Solution

The correct option is D
$\frac{x^{2}}{32} + \frac{y^{2}}{30}$ = 1

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

The correct option is D x232+y230 = 1 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
$\frac{x^{2}}{32} + \frac{y^{2}}{30}$ = 1

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