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The angle between a pair of tangents drawn from a point P to the circle x2 +y2 +4x –6y +9 sin2 ( + 13 cos2 ( =0 is 2(. The equation of the locus of the point P is

x2 +y2 +4x –6y +4=0

x2 +y2 +4x –6y –9 =0

x2 +y2 +4x –6y –4 =0

x2 +y2 +4x –6y +9 =0

Let AB be a chord of the circle x2 +y2 =r2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as P moves on the circle is

a parabola

a circle

an ellipse

a pair of straight lines

If two distinct chords, drawn from the point (p, q) on the circle x2 + y2 =px +qy (where pq ( 0) are bisected by the x-axis, then

p2 =q2

p2 =8q2

p2 <8q2

p2 >8q2

The centre of circle inscribed in square formed by the lines x2 -8x +12=0 and y2 -14y +45 =0, is

(4,7)

(7,4

(9,4)

(4,9)

The equations of the tangents drawn from the origin to the circle x2 +y2 -2rx -2hy +h2=0, are

x =0

y =0

(h2 –r2)x -2hy =0

(h2 +r2)x +2hy =0

1 and 3

2 and 4

If the circle x2 +y2 =a2 intersects the hyperbola xy =c2 in four points P(x1, y1), Q(x2, y2), R(x3, y3), S(x4, y4), then

x1+x2+x3+x4=0

y1+y2+y3+y4=0

x1x2x3x4 = c4

y1y2y3y4= c4

All of above

A circle is given by x2 +(y-1)2 =1, another circle C touches it externally and also the x-axis, then the locus of its centre is

{(x, y): x2 =4y} ( {(x, y): y<0}

{(x, y): x2 +(y-1)2=4} ( {(x, y): y(0}

{(x, y): x2 =y} ( {(0, y): y(0}

{(x, y): x2 =4y} ( {(0, y): y(0}

The number of common tangents to the circle x2 +y2 =4 and x2 +y2 -6x -8y =24 is

0

1

3

4

The circles x2 +y2 -10x + 16=0 and x2 +y2 =r2 intersect each other in two distinct points if

r<2

r>8

2 2( r (8

The lines 2x –3y =5 and 3x –4y =7 are diameters of a circle of area 154 sq. Then the equation of this circle is

x2+ y2 +2x –2y =62

x2+ y2 +2x –2y =47

x2+ y2 -2x +2y =47

x2+ y2 -2x +2y =62

x2 +y2 +4x –6y +4=0

x2 +y2 +4x –6y –9 =0

x2 +y2 +4x –6y –4 =0

x2 +y2 +4x –6y +9 =0

Let AB be a chord of the circle x2 +y2 =r2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as P moves on the circle is

a parabola

a circle

an ellipse

a pair of straight lines

If two distinct chords, drawn from the point (p, q) on the circle x2 + y2 =px +qy (where pq ( 0) are bisected by the x-axis, then

p2 =q2

p2 =8q2

p2 <8q2

p2 >8q2

The centre of circle inscribed in square formed by the lines x2 -8x +12=0 and y2 -14y +45 =0, is

(4,7)

(7,4

(9,4)

(4,9)

The equations of the tangents drawn from the origin to the circle x2 +y2 -2rx -2hy +h2=0, are

x =0

y =0

(h2 –r2)x -2hy =0

(h2 +r2)x +2hy =0

1 and 3

2 and 4

If the circle x2 +y2 =a2 intersects the hyperbola xy =c2 in four points P(x1, y1), Q(x2, y2), R(x3, y3), S(x4, y4), then

x1+x2+x3+x4=0

y1+y2+y3+y4=0

x1x2x3x4 = c4

y1y2y3y4= c4

All of above

A circle is given by x2 +(y-1)2 =1, another circle C touches it externally and also the x-axis, then the locus of its centre is

{(x, y): x2 =4y} ( {(x, y): y<0}

{(x, y): x2 +(y-1)2=4} ( {(x, y): y(0}

{(x, y): x2 =y} ( {(0, y): y(0}

{(x, y): x2 =4y} ( {(0, y): y(0}

The number of common tangents to the circle x2 +y2 =4 and x2 +y2 -6x -8y =24 is

0

1

3

4

The circles x2 +y2 -10x + 16=0 and x2 +y2 =r2 intersect each other in two distinct points if

r<2

r>8

2

The lines 2x –3y =5 and 3x –4y =7 are diameters of a circle of area 154 sq. Then the equation of this circle is

x2+ y2 +2x –2y =62

x2+ y2 +2x –2y =47

x2+ y2 -2x +2y =47

x2+ y2 -2x +2y =62

AIEEE Mathematics IIT JEE Mathematics CBSE AIEEE Mathematics: Circles and Family of Circles Circles and Family of Circles

hey! how to do ques 5.. i got x=0 as tangent but not the other one and also ques 2 the hyperbola ques.

thanks.. :)

2807 days 1 hours 33 minutes ago

got 9 right think so answer of ques 1 is d but its given b

3979 days 16 hours 53 minutes ago

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