If P is any point on the director circle, then the locus of middle point of the chord in which the polar of P cuts the ellipse x2/a2+y2/b2=1 is

1.  (x2/a2+y2/b2)2= x2 +y2/a2+b2

2.  (x2/a2-y2/b2)2= x2 +y2/a2+b2

3.  (x2/a2+y2/b2)2= x2 -y2/a2+b2

4.  (x2/a2+y2/b2)2= x2 -y2/a2-b2

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4
Correct Answer :

(x2/a2+y2/b2)2= x2 +y2/a2+b2


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An aeroplane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of two planes from the same point on the ground are 600 and 450

1.  100√3

2.  100/√3

3.  50

4.  150(√3+1)

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4
Correct Answer :

100√3


Explanation :
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From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be α and β. The height of the aeroplane above the

1.  

2.  

3.  

4.  none

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4
Correct Answer :


Explanation :
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The condition that the chord of the ellipse x2/a2+y2/b2=1 whose middle point is (x1, y1) subtends right angle at the centre of the ellipse is

1.  

2.  

3.  

4.  

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Correct Answer :


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1.  0

2.  1

3.  1/12

4.  -1/12

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Correct Answer :

1/12


Explanation :
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The equation of the locus of the middle point of the portion of a tangent to the ellipse x2/a2+y2/b2=1  included between the axes is

1.  a2x2+b2y2=4x2y2

2.  b2x2+a2y2=4x2y2

3.  a2x2-b2y2=4x2y2

4.  b2x2-b2y2=4x2y2

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4
Correct Answer :

b2x2+a2y2=4x2y2


Explanation :
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The equation of the chord of the ellipse 2x2+3y2=6 having (1, -1) as its midpoint is

1.  8x+9y-25=0

2.  2x-3y-5=0

3.  x+y-1=0

4.  3x-2y-6=0

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4
Correct Answer :

2x-3y-5=0


Explanation :
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1.  0

2.  1

3.  2

4.  1/2

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4
Correct Answer :

1/2


Explanation :
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The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1  which touch concentric circle of radius c is

1.  c2(x2/a4+y2/b4)=(x2/a2+y2/b2)2

2.  c2(x2/a4+y2/b4)=(x2/a2-y2/b2)2

3.  c2(x2/a4-y2/b4)=(x2/a2+y2/b2)2

4.  c2(x2/a4-y2/b4)=(x2/a2-y2/b2)2

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4
Correct Answer :

c2(x2/a4+y2/b4)=(x2/a2+y2/b2)2


Explanation :
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The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   that touch the circle x2+y2=b2

1.  (x2/a2+y2/b2)2= x2/a4+y2/b4

2.  (x2/a2+y2/b2)2= b2 (x2/a4+y2/b4)

3.  (x2/a2+y2/b2)2= a2 (x2/a4+y2/b4)

4.  none

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4
Correct Answer :

(x2/a2+y2/b2)2= b2 (x2/a4+y2/b4)


Explanation :
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