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 |
C) \( \Large x^{2}+y^{2}-2x-4y-3=0 \) |
Let the equation of the concentric circle \( \Large b\ x^{2}+y^{2}-2x-4y+n=0 \) it passes through \( \Large \left(3,\ 4\right) \)
\( \Large 3^{2}+4^{2}-2 \left(3\right)-4 \left(4\right)+n=0 \)
n = -3
Thus the equation of concentric circle is
\( \Large x^{2}+y^{2}-2x-4y-3=0 \)
1). Circle \( \Large x^{2}+y^{2}-2x-nx-1=0 \) passes through two fixed points, co-ordinates of the points are
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2). Centre of circle whose normals are \( \Large x^{2}-2xy-3x+6y=0 \) is
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3). 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:
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4). 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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5). AB, is a diameter of a circle and c is any point on circumference of the circle then:
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6). The number of common tangents to the circles \( \Large x^{2}+y^{2}-2x-4y+1=0 \) and \( \Large x^{2}+y^{2}-12x-16y+91=0 \) is
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7). A, B, C and D are the points of intersection with the co-ordinate axes of the lines \( \Large ax+by=ab\ and\ bx+ay=ab \) then:
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8). The gradient of the radical axis of the circles \( \Large x^{2}+y^{2}-3x-4y+5=0\ and\ 3x^{2}+3y^{2}-7x+8y+11=0 \) is
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9). The limiting point of the system of circles represented by the equation \( \Large 2\left(x^{2}+y^{2}\right)+nx+\frac{9}{2}=0 \) are
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10). The radical centre of the circles \( \Large x^{2}+y^{2}-16x+60=0,\) \( \Large x^{2}+y^{2}-12x+27=0,\) \( \Large x^{2}+y^{2}-12y+8=0 \) is
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