A point P on an ellipse is at a distance 6 units from a focus- If the eccentricity of the ellipse is 35- then the distance of P from the corresponding directrix is

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Directrix of Ellipse

A point P o...

Question

A point $P$ on an ellipse is at a distance $6$ units from a focus. If the eccentricity of the ellipse is $\frac{3}{5}$ , then the distance of P from the corresponding directrix is

\frac{8}{5}

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\frac{5}{8}

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10

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12

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Solution

The correct option is C $10$
Let the focus be $S$ and $M$ be any point on the directrix
then by basic definition $P S = e P M$
$\Rightarrow 6 = \frac{3}{5} P M \Rightarrow P M = \frac{30}{3} = 10$
So the distance of $P$ from directrix is $10$
Option $C$ is correct.

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A point P on an ellipse is at a distance 6 units from a focus. If the eccentricity of the ellipse is 35, then the distance of P from the corresponding directrix is

The correct option is C 10Let the focus be S and M be any point on the directrixthen by basic definition PS=ePM⇒6=35PM⇒PM=303=10So the distance of P from directrix is 10Option C is correct.

A point $P$ on an ellipse is at a distance $6$ units from a focus. If the eccentricity of the ellipse is $\frac{3}{5}$ , then the distance of P from the corresponding directrix is

The correct option is C $10$
Let the focus be $S$ and $M$ be any point on the directrix
then by basic definition $P S = e P M$
$\Rightarrow 6 = \frac{3}{5} P M \Rightarrow P M = \frac{30}{3} = 10$
So the distance of $P$ from directrix is $10$
Option $C$ is correct.