Question

Is it possible for
x2/4 + y2 /9 = 1 to have foci at (−c, 0) and (c, 0) for some real number c?

Answer 1

Answer:No

Explanation:

Given

Equation of ellipse

`(x^2)/(4)+(y^2)/(9)=1`

this is the equation of a vertical Ellipse

which is in the form of
`(x^2)/(b^2)+(y^2)/(a^2)=1`

and its eccentricity is given by

`e=\sqrt{1-(b^2)/(a^2)}`

`e=\sqrt{1-(4)/(9)}=\sqrt{(5)/(9)}=(√(5))/(3)`

and Focii of Vertical ellipse is
`(0,\pm ae)`

`ae=3* (√(5))/(3)=√(5)`

Focii are
`(0,\pm √(5))`

so (-c,0) and (c,0) cannot be the focii of ellipse
`(x^2)/(4)+(y^2)/(9)=1`