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1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $$10\,\pi $$, then the equation of the circle is
A
$${x^2}\, + \,{y^2} + \,2x\, - \,2y - \,23\,\, = 0$$
B
$${x^2}\, + \,{y^2} - \,2x\, - \,2y - \,23\,\, = 0$$
C
$${x^2}\, + \,{y^2} + \,2x\, + \,2y - \,23\,\, = 0$$
D
$${x^2}\, + \,{y^2} - \,2x\, + \,2y - \,23\,\, = 0$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = 4$$ orthogonally, then the locus of its centre is
A
$$2ax\, - 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$$
B
$$2ax\, + 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$$
C
$$2ax\, - 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$$
D
$$2ax\, + 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$$
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
A
$${(y\, - \,q)^2} = \,4\,px$$
B
$${(x\, - \,q)^2} = \,4\,py$$
C
$${(y\, - \,p)^2} = \,4\,qx$$
D
$${(x\, - \,p)^2} = \,4\,qy$$
4
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. Equation of the circle on AB as a diameter is
A
$$\,{x^2}\, + \,{y^2} + \,x\, - \,y\,\, = 0$$
B
$$\,{x^2}\, + \,{y^2} - \,x\, + \,y\,\, = 0$$
C
$$\,{x^2}\, + \,{y^2} + \,x\, + \,y\,\, = 0$$
D
$$\,{x^2}\, + \,{y^2} - \,x\, - \,y\,\, = 0$$
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