11). The equations of the tangents to the circle \( \Large x^{2}+y^{2}-6x+4y-12=0 \) which are parallel to the line \( \Large 4x+3y+5=0 \),are
A). \( \Large 4x+3y+11=0 \) and \( \Large 4x+3y+8=0 \) |
B). \( \Large 4x+3y-9=0 \) and \( \Large 4x+3y+7=0 \) |
C). \( \Large 4x+3y+19=0 \) and \( \Large 4x+3y-31=0 \) |
D). \( \Large 4x+3y-10=0 \) and \( \Large 4x+3y+12=0 \) |
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12). The lines \( \Large 2x-3y=5\ and\ 3x-4y=7 \) are diameters of a circle having area as 154 sq unit. Then the equation of the circle is:
A). \( \Large x^{2}+y^{2}+2x-2y=62 \) |
B). \( \Large x^{2}+y^{2}+2x-2y=47 \) |
C). \( \Large x^{2}+y^{2}-2x+2y=47 \) |
D). \( \Large x^{2}+y^{2}-2x+2y=62 \) |
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13). The pole of the straight line \( \Large x+2y=1 \) with respect to the circle \( \Large x^{2}+y^{2}=5 \) is:
A). \( \Large \left(5,\ 5\right) \) |
B). \( \Large \left(5,\ 10\right) \) |
C). \( \Large \left(10,\ 5\right) \) |
D). \( \Large \left(10,\ 10\right) \) |
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14). If the circle \( \Large x^{2}+y^{2}+6x-2y+k=0 \) bisects the circumference of the circle \( \Large x^{2}+y^{2}+2x-6y-15=0 \) then k is equal to:
A). 21 |
B). -21 |
C). 23 |
D). -23 |
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15). If \( \Large 5x-12y=10 \) and \( \Large 12y-5x+16=0 \) are two tangents to a circle, then the radius of the circle is
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16). Equation of the circle passing through the point \( \Large \left(3,\ 4\right) \) and concentric with the circle \( \Large x^{2}+y^{2}-2x-4y+1=0 \) is
A). \( \Large x^{2}+y^{2}-2x-4y=0 \) |
B). \( \Large x^{2}+y^{2}-2x-4y+3=0 \) |
C). \( \Large x^{2}+y^{2}-2x-4y-3=0 \) |
D). none of the above |
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17). Circle \( \Large x^{2}+y^{2}-2x-nx-1=0 \) passes through two fixed points, co-ordinates of the points are
A). \( \Large \left(0,\ \pm 1\right) \) |
B). \( \Large \left(\pm\ 1,\ 0\right) \) |
C). \( \Large \left(0,\ 1\right)\ and\ \left(0,\ 2\right) \) |
D). \( \Large \left(0,\ -1\right)\ and\ \left(0,\ -2\right) \) |
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18). Centre of circle whose normals are \( \Large x^{2}-2xy-3x+6y=0 \) is
A). \( \Large \left(3,\ \frac{3}{2}\right) \) |
B). \( \Large \left(3,\ -\frac{3}{2}\right) \) |
C). \( \Large \left(\frac{3}{2},\ 3\right) \) |
D). none of these |
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19). The locus of centre of a circle \( \Large x^{2}+y^{2}-2x-2y+1=0 \) which rolls outside the circle \( \Large x^{2}+y^{2}-6x+8y=0 \) is:
A). \( \Large x^{2}+y^{2}-2x-2y-34=0 \) |
B). \( \Large x^{2}+y^{2}-6x+8y+11=0 \) |
C). \( \Large x^{2}+y^{2}-6x+8y-11=0 \) |
D). none of these |
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20). A line through \( \Large P \left(1,\ 4\right) \) intersect a circle \( \Large x^{2}+y^{2}=16 \) at A and B, then PA-PB is equal to:
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