Find the eccentricity of an ellipse in which distance between the foci is $10$ and that of focus and corresponding directrix is $15.$

\frac{1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{1}{2}$
Distance between foci $= 2 a e = 10$ (given) $\Rightarrow a e = 5$ (i)
And distance between focus and corresponding directrix is $= \frac{a}{e} - a e = 15$ (given)
Now using (i)
$\frac{a}{e} = 20 \Rightarrow e^{2} = \frac{1}{4} \Rightarrow e = \frac{1}{2}$

Suggest Corrections

Similar questions

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $\frac{1}{2}$ , then length of the minor axis is

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $\frac{1}{2}$ ,

then length of the minor axis is

Q. If in an ellipse, a focus is

(6, 7)

, the corresponding directrix is

x + y + 2 = 0

and the eccentricity =

\frac{1}{2},

then the equation of the ellipse is:

Q. The foci of an ellipse are

S (- 2, - 3), S^{'} (0, 1)

and its

e = \frac{1}{\sqrt{2}}

then the directrix corresponding to the focus

S^{'}

is:

Q. Find the equation of the ellipse whose focus is

(1, - 1)

eccentricity is

\frac{2}{3}

and directrix is

x + y + 2 = 0

Join BYJU'S Learning Program

Find the eccentricity of an ellipse in which distance between the foci is 10 and that of focus and corresponding directrix is 15.

The correct option is B 12Distance between foci =2ae=10 (given) ⇒ae=5 (i)And distance between focus and corresponding directrix is =ae−ae=15 (given)Now using (i)ae=20⇒e2=14⇒e=12

Find the eccentricity of an ellipse in which distance between the foci is $10$ and that of focus and corresponding directrix is $15.$

The correct option is B $\frac{1}{2}$
Distance between foci $= 2 a e = 10$ (given) $\Rightarrow a e = 5$ (i)
And distance between focus and corresponding directrix is $= \frac{a}{e} - a e = 15$ (given)
Now using (i)
$\frac{a}{e} = 20 \Rightarrow e^{2} = \frac{1}{4} \Rightarrow e = \frac{1}{2}$