The distance of the point Px1-5 from the foci of the ellipse x29-y225-1 are where P lies on ellipse

Ii's major axis is parallel to y axis Equation of ellipse x^2a^2+y^2b^2=1 ∴ a=3, b=5⇒ e=45 Distance from the foci is d=b± ey_1 ⇒ d=5±4=1,9 unit ...

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Standard XII

Mathematics

Eccentricity of Ellipse

The distance ...

Question

The distance of the point $P (x_{1}, 5)$ from the foci of the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$ are (where $P$ lies on ellipse)

2

unit

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9

unit

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1

unit

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7

unit

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Solution

The correct option is C $1$ unit
Ii's major axis is parallel to $y -$ axis
Equation of ellipse
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
$∴ a = 3, b = 5 \Rightarrow e = \frac{4}{5}$
Distance from the foci is
$d = b \pm e y_{1}$
$\Rightarrow d = 5 \pm 4 = 1, 9$ unit

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Similar questions

Q. The distance of the point

P (x_{1}, 5)

from the foci of the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1

are (where

P

lies on ellipse)

Q. Let

S

and

S^{'}

be the two foci of the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1.

If the circle described on

S S^{'}

as diameter touches the ellipse in real points, then

6 e^{2} =

(where

e

is eccentricity of ellipse)

Q. The distances from the foci to a point

P (x_{1}, y_{1})

on the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1

are :

Q. The foci of the ellipse

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

and the hyperbola

\frac{x^{2}}{144} - \frac{y^{2}}{81} = \frac{1}{25}

coincide. Then , the value of

b^{2}

is :

Q. The foci of the ellipse

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

and the hyperbola

\frac{x^{2}}{144} - \frac{y^{2}}{81} = 1

\frac{1}{25}

coincide . Then the value of b

^{2}

is:

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The distance of the point P(x1,5) from the foci of the ellipse x29+y225=1 are (where P lies on ellipse)

The correct option is C 1 unitIi's major axis is parallel to y−axis Equation of ellipse x2a2+y2b2=1 ∴ a=3, b=5⇒ e=45 Distance from the foci is d=b±ey1 ​​​​​​​⇒d=5±4=1,9 unit

The distance of the point $P (x_{1}, 5)$ from the foci of the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$ are (where $P$ lies on ellipse)

The correct option is C $1$ unit
Ii's major axis is parallel to $y -$ axis
Equation of ellipse
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
$∴ a = 3, b = 5 \Rightarrow e = \frac{4}{5}$
Distance from the foci is
$d = b \pm e y_{1}$
$\Rightarrow d = 5 \pm 4 = 1, 9$ unit