IIT-JEE 2010 Paper 2 Offline | Ellipse Question 17 | Mathematics

1

IIT-JEE 2010 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-1

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$B$$.

The orthocentre of the triangle $$PAB$$ is

A

$$\left( {5,{8 \over 7}} \right)$$

B

$$\left( {{7 \over 5},{{25} \over 8}} \right)$$

C

$$\left( {{11 \over 5},{{8} \over 5}} \right)$$

D

$$\left( {{8 \over 25},{{7} \over 5}} \right)$$

2

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

The normal at a point $$P$$ on the ellipse $${x^2} + 4{y^2} = 16$$ meets the $$x$$- axis $$Q$$. If $$M$$ is the mid point of the line segment $$PQ$$, then the locus of $$M$$ intersects the latus rectums of the given ellipse at the points

A

$$\left( { \pm {{3\sqrt 5 } \over 2},\, \pm {2 \over 7}} \right)$$

B

$$\left( { \pm {{3\sqrt 5 } \over 2},\, \pm \sqrt {{{19} \over 4}} } \right)$$

C

$$\left( { \pm 2\sqrt 3 , \pm {1 \over 7}} \right)$$

D

$$\left( { \pm 2\sqrt 3 , \pm {{4\sqrt 3 } \over 7}} \right)$$

3

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)

4

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

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