For the ellipse x24-y21-1 and circle x-12-y-22-3- the centre of the circle lies

Centre of the circle is (1, 2) we have, S_1=14+41 1 gt;0 ⇒ The centre nbsp;of the circle lies outside the ellipse nbsp; ...

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Standard XI

Mathematics

Position of a Line W.R.T Ellipse

For the ellip...

Question

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

inside the ellipse

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outside the ellipse

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on the ellipse

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none of these

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Solution

The correct option is B outside the ellipse
Centre of the circle is $(1, - 2)$
we have,
$S_{1} = \frac{1}{4} + \frac{4}{1} - 1 > 0$
$\Rightarrow$ The centre of the circle lies outside the ellipse

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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. 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. The length of the common chord of the ellipse

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

and the circle

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

is:

Q. The length of the common chord of the ellipse

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

and the circle

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

is:

Q. Let

P, Q, R

be the points on the auxiliary circle of ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b)

, such that

P Q R

is an equilateral triangle and

P^{'} Q^{'} R^{'}

is corresponding triangle inscribed within the ellipse. Then centroid of the triangle

P^{'} Q^{'} R^{'}

lies at

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Position of a Line W.R.T Ellipse

Standard XI Mathematics

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For the ellipse x24+y21=1 and circle (x−1)2+(y+2)2=3, the centre of the circle lies

The correct option is B outside the ellipse Centre of the circle is (1,−2) we have, S1=14+41−1>0 ⇒ The centre of the circle lies outside the ellipse

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

The correct option is B outside the ellipse
Centre of the circle is $(1, - 2)$
we have,
$S_{1} = \frac{1}{4} + \frac{4}{1} - 1 > 0$
$\Rightarrow$ The centre of the circle lies outside the ellipse