Releted MCQ Question on
Geometry >> Ellipse
Releted Question 1
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 $$\left( {1,\,2} \right)$$ and $$\left( {2,\,1} \right)$$ respectively. Then-
A.
$$Q$$ lies inside $$C$$ but outside $$E$$
B.
$$Q$$ lies outside both $$C$$ and $$E$$
C.
$$P$$ lies inside both $$C$$ and $$E$$
D.
$$P$$ lies inside $$C$$ but outside $$E$$
Releted Question 2
The radius of the circle passing through the foci of the ellipse $$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1,$$ and having its centre at $$\left( {0,\,3} \right)$$ is-
A.
$$4$$
B.
$$3$$
C.
$$\sqrt {\frac{1}{2}} $$
D.
$$\frac{7}{2}$$
Releted Question 3
The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1,$$ is-
A.
$$\frac{{27}}{4}\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
B.
$$9\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
C.
$$\frac{{27}}{2}\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
D.
$$27\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
Releted Question 4
If tangents are drawn to the ellipse $${x^2} + 2{y^2} = 2,$$ then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is-
A.
$$\frac{1}{{2{x^2}}} + \frac{1}{{4{y^2}}} = 1$$
B.
$$\frac{1}{{4{x^2}}} + \frac{1}{{2{y^2}}} = 1$$
C.
$$\frac{{{x^2}}}{2} + \frac{{{y^2}}}{4} = 1$$
D.
$$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{2} = 1$$
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Ellipse