Question

The eccentricity of the ellipse y² + 4x² - 12x + 6y + 14 = 0 is ______.

विकल्प

• `1/sqrt2`

• `1/2`

• `sqrt3/2`

• `1/sqrt3`

Answer 1

The eccentricity of the ellipse y² + 4x² - 12x + 6y + 14 = 0 is `sqrt3/2`.

Explanation:

Given ellipse,

`y^2+4x^2-12x+6y+14=0`

`4x^2-12x+y^2+6y+14=0`

`4(x^2-3x+9/4)+y^2+6y+9=-14+9+9`

`4(x-3/2)^2+(y+3)^2=4`

`((x-3/2)^2)/1+(y+3)^2/4=1`

Here, a² = 1, b² = 4

`therefore     e=sqrt(1-a^2/b^2)`

`e=sqrt(1-1/4)`

`=sqrt3/2`