The position of the point 2-3 with respect to the ellipse x2-9-y2-25-1-A- It lies on the ellipseB- It lies outside the ellipseC- It lies inside the ellipseD- None of these

The correct option is C It lies inside the ellipseEquation 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) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

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

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

It lies outside the ellipse

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

It lies inside the ellipse

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

None of these

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

Open in App

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

Suggest Corrections

Similar questions

Q. For the ellipse

\frac{x^{2}}{4} + \frac{y^{2}}{1} = 1

and circle

(x - 1)^{2} + (y + 2)^{2} = 3,

the centre of the circle lies

Q. Let

E

be the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

and

C

be the circle

x^{2} + y^{2} = 9

. Let

P

and

Q

be the points

(1, 2)

and

(2, 1)

respectively. Then

Q. For the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

, the point

(5 cos θ, 5 sin θ)

lies on its:

Q. Which of the following points lies inside the ellipse

9 (x - 1)^{2} + 16 y^{2} = 25

Find the set of value(s) for which the point P(a,-a) lies inside the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ .

Join BYJU'S Learning Program

Explore more

Position of a Point W.R.T Ellipse

Standard XII Mathematics

Join BYJU'S Learning Program

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