The lengths of the chords of the circle x2+y2-2x-6y-15=0 which make an angle of 600 at (1, 3) and the locus of the midpoints of all such chords are

1.  5, 4(x2+y2-2x-6y)-35=0

2.  10, (x2+y2-2x-6y)-135=0

3.  15, 4(x2+y2-2x-6y)-35=0

4.  3, 4(x2+y2+2x+6y)-35=0

View Answer  
4
Correct Answer :

5, 4(x2+y2-2x-6y)-35=0


Explanation :
No Explanation available for this question

From the point A(0,3) on the circle x2+4x+(y-3)2=0, a chord, AB is drawn and extended to a point P, such that AP = 2AB. The locus of P is

1.  x2+4x+(y-3)2=0

2.  x2+8x+(y-3)2=0

3.  x2+4x-(y-3)2=0

4.  x2+8x-(y-3)2=0

View Answer  
4
Correct Answer :

x2+8x+(y-3)2=0


Explanation :
No Explanation available for this question

The locus of the midpoints of the chords of the circle 4x2+4y2-12x+4y+1=0 which subtend an angle of π/3 at its centre is a circle of radius

1.  3/4

2.   3√3/4

3.  3/2

4.  4√3

View Answer  
4
Correct Answer :

 3√3/4


Explanation :
No Explanation available for this question

The locus of the midpoint of the chord of the circle x2+y2-2x-2y-2=0, which makes an angle of 1200 at the centre is

1.  x2+y2-2x-2y+1=0

2.  x2+y2+x+y-1=0

3.  x2+y2-2x-2y-1=0

4.  none

View Answer  
4
Correct Answer :

x2+y2-2x-2y+1=0


Explanation :
No Explanation available for this question

(a, b) is the midpoint of the chord AB of the circle x2+y2=r2. The tangents at  A, B meet at C, then area of ΔABC=

1.  ((a2+b2+r2)3/2)/√ a2+b2

2.  ((r2-a2-b2)3/2)/√ a2+b2

3.  ((a2-b2-r2)3/2)/√ a2+b2

4.  none

View Answer  
4
Correct Answer :

((r2-a2-b2)3/2)/√ a2+b2


Explanation :
No Explanation available for this question

The equation to the pail of tangents drawn from (10, 4) to the circle x2+y2=25 is

1.  9x2+80xy-75y2-500x-200y+2900=0

2.  9x2-15y2-6x+60y-51=0

3.  16x2+20xy-5y2-36x+90y-261=0

4.  3x2-10xy+3y2=0

View Answer  
4
Correct Answer :

9x2+80xy-75y2-500x-200y+2900=0


Explanation :
No Explanation available for this question

The equation to the pair of tangents drawn from (3, 2) to the circle x2+y2-6x+4y-2=0 is

1.  9x2+80xy-75y2-500x-200y+2900=0

2.  9x2-15y2-6x+60y-51=0

3.  16x2+20xy-5y2-36x+90y-261=0

4.  3x2-10xy+3y2=0

View Answer  
4
Correct Answer :

9x2-15y2-6x+60y-51=0


Explanation :
No Explanation available for this question

The equations of the tangents drawn from the origin x2+y2+2gx+2fy+f2=0 is

1.  x=0, (f2-g2)x-2fgy=0

2.  x=0, (f2+2g2)x-2fgy=0

3.  x=2, (2f2+3g2)x+2fgy=0

4.  x=5, (3f2+5g2)x+2fgy=0

View Answer  
4
Correct Answer :

x=0, (f2-g2)x-2fgy=0


Explanation :
No Explanation available for this question

The angle between the tangents drawn from (0,0) to the circle x2+y2+4x-6y+4=0 is

1.  Sin-1 5/13

2.  Sin-1 5/12

3.  Sin-1 12/13

4.   π/2

View Answer  
4
Correct Answer :

Sin-1 12/13


Explanation :
No Explanation available for this question

If θ is the angle between the tangents from (- 1,0) to the circle x2+y2-5x+4y-2=0, then θ=

1.  2 Tan-1(7/4)

2.  Tan-1(7/4)

3.  2 Cot-1(7/4)

4.  Cot-1(7/4)

View Answer  
4
Correct Answer :

2 Tan-1(7/4)


Explanation :
No Explanation available for this question
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