The position of the point 2- -3 with respect to the ellipse x29-y225-1- is

Equation of the ellipse is x^29+y^225=1 S_1=2^29+( 3)^225 1 ⇒ S_1= 44225 lt;0. Therefore, the point (2, 3) lies inside the ellipse ...

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Standard XIII

Mathematics

Position of a Point W.R.T Ellipse

The position ...

Question

The position of the point $(2, - 3)$ with respect to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1,$ is

It lies on the ellipse

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It lies outside the ellipse

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It lies inside the ellipse

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None of these

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Solution

The correct option is C It lies inside the ellipse
Equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$
$S_{1} = \frac{2^{2}}{9} + \frac{(- 3)^{2}}{25} - 1$
$\Rightarrow S_{1} = - \frac{44}{225} < 0.$
Therefore, the point $(2, - 3)$ lies inside the ellipse

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Position of a Point W.R.T Ellipse

Standard XIII Mathematics

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The position of the point (2,−3) with respect to the ellipse x29+y225=1, is

The correct option is C It lies inside the ellipseEquation of the ellipse is x29+y225=1 S1=229+(−3)225−1 ⇒S1=−44225<0. Therefore, the point (2,−3) lies inside the ellipse

The position of the point $(2, - 3)$ with respect to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1,$ is

The correct option is C It lies inside the ellipse
Equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$
$S_{1} = \frac{2^{2}}{9} + \frac{(- 3)^{2}}{25} - 1$
$\Rightarrow S_{1} = - \frac{44}{225} < 0.$
Therefore, the point $(2, - 3)$ lies inside the ellipse