An ellipse has eccentricity $$\frac{1}{2}$$ and one focus at the point$$P\left( \frac{1}{2},\ 1 \right)$$. Its one directrix is the common tangent nearer to the point P, to the circle $${{x}^{2}}+{{y}^{2}}=1$$ and the hyperbola$${{x}^{2}}-{{y}^{2}}=1$$. The equation of the ellipse in the standard form, is [IIT 1996]

Question

An ellipse has eccentricity $$\frac{1}{2}$$ and one focus at the point$$P\left( \frac{1}{2},\ 1 \right)$$. Its one directrix is the common tangent nearer to the point P, to the circle $${{x}^{2}}+{{y}^{2}}=1$$ and the hyperbola$${{x}^{2}}-{{y}^{2}}=1$$. The equation of the ellipse in the standard form, is       [IIT 1996]

TuteeHUB · Accepted Answer

$$\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y+1)}^{2}}}{1/12}=1$$

TuteeHUB · Answer

$$\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y-1)}^{2}}}{1/12}=1$$

TuteeHUB · Answer

$$\frac{{{(x-1/3)}^{2}}}{1/9}-\frac{{{(y-1)}^{2}}}{1/12}=1$$

TuteeHUB · Answer

$$\frac{{{(x-1/3)}^{2}}}{1/9}-\frac{{{(y+1)}^{2}}}{1/12}=1$$

1.	An ellipse has eccentricity \[\frac{1}{2}\] and one focus at the point\[P\left( \frac{1}{2},\ 1 \right)\]. Its one directrix is the common tangent nearer to the point P, to the circle \[{{x}^{2}}+{{y}^{2}}=1\] and the hyperbola\[{{x}^{2}}-{{y}^{2}}=1\]. The equation of the ellipse in the standard form, is [IIT 1996]
A.	\[\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y-1)}^{2}}}{1/12}=1\]
B.	\[\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y+1)}^{2}}}{1/12}=1\]
C.	\[\frac{{{(x-1/3)}^{2}}}{1/9}-\frac{{{(y-1)}^{2}}}{1/12}=1\]
D.	\[\frac{{{(x-1/3)}^{2}}}{1/9}-\frac{{{(y+1)}^{2}}}{1/12}=1\]
Answer» B. \[\frac{{{(x-1/3)}^{2}}}{1/9}+\frac{{{(y+1)}^{2}}}{1/12}=1\]

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