IIT-JEE 2009 Paper 1 Offline | Ellipse Question 21 | Mathematics

1

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

The line passing through the extremity $$A$$ of the major axis and extremity $$B$$ of the minor axis of the ellipse $${x^2} + 9{y^2} = 9$$ meets its auxiliary circle at the point $$M$$. Then the area of the triangle with vertices at $$A$$, $$M$$ and the origin $$O$$ is

A

$${{31} \over {10}}$$

B

$${{29} \over {10}}$$

C

$${{21} \over {10}}$$

D

$${{27} \over {10}}$$

2

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-0

Match the conics in Column I with the statements/expressions in Column II :

	Column I		Column II
(A)	Circle	(P)	The locus of the point ($$h,k$$) for which the line $$hx+ky=1$$ touches the circle $$x^2+y^2=4$$.
(B)	Parabola	(Q)	Points z in the complex plane satisfying $$\|z+2\|-\|z-2\|=\pm3$$.
(C)	Ellipse	(R)	Points of the conic have parametric representation $$x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),y = {{2t} \over {1 + {t^2}}}$$
(D)	Hyperbola	(S)	The eccentricity of the conic lies in the interval $$1 \le x \le \infty $$.
		(T)	Points z in the complex plane satisfying $${\mathop{\rm Re}\nolimits} {(z + 1)^2} = \|z{\|^2} + 1$$.

A

(A)$$\to$$(P); (B)$$\to$$(S), (T); (C)$$\to$$(R); (D)$$\to$$(R), (S)

B

(A)$$\to$$(P); (B)$$\to$$(S), (T); (C)$$\to$$(R); (D)$$\to$$(Q), (S)

C

(A)$$\to$$(P); (B)$$\to$$(S), (T); (C)$$\to$$(S); (D)$$\to$$(R), (S)

D

(A)$$\to$$(P); (B)$$\to$$(P), (T); (C)$$\to$$(R); (D)$$\to$$(Q), (S)

3

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,

A

$${C_1}$$ and $${C_2}$$ touch each other only at one point.

B

$${C_1}$$ and $${C_2}$$ touch each other exactly at two points

C

$${C_1}$$ and $${C_2}$$ intersect (but do not touch ) at exactly two points

D

$${C_1}$$ and $${C_2}$$ neither intersect nor touch each other

4

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

+2

-0.5

The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and coordinate axes is

A

$$ab$$ sq. units

B

$${{{{a^2} + {b^2}} \over 2}}$$ sq. units

C

$${{{{\left( {a + b} \right)}^2}} \over 2}$$ sq. units

D

$${{{a^2} + ab + {b^2}} \over 3}$$ sq. units