Circles · JEE Main previous year questions

2004 4 questions

1. Q172004 · 24 Apr 2004 · Shift 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 :

   1. A.$2ax-2by-(a^2+b^2+4)=0$
   2. B.$2ax+2by-(a^2+b^2+4)=0$
   3. C.$2ax-2by+(a^2+b^2+4)=0$
   4. D.$2ax+2by+(a^2+b^2+4)=0$
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   Answer: B

2. Q182004 · 24 Apr 2004 · Shift 1

   If the lines $2x+3y+1=0$ and $3x-y-4=0$ lie along diameters of a circle of circumference $10\pi$, then the equation of the circle is :

   1. A.$x^2+y^2+2x-2y-23=0$
   2. B.$x^2+y^2-2x-2y-23=0$
   3. C.$x^2+y^2+2x+2y-23=0$
   4. D.$x^2+y^2-2x+2y-23=0$
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   Answer: D

3. Q192004 · 24 Apr 2004 · Shift 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 :

   1. A.$x^2+y^2+x-y=0$
   2. B.$x^2+y^2-x+y=0$
   3. C.$x^2+y^2+x+y=0$
   4. D.$x^2+y^2-x-y=0$
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   Answer: D

4. Q572004 · 24 Apr 2004 · Shift 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 :

   1. A.$(y-q{)}^2=4px$
   2. B.$(x-q{)}^2=4py$
   3. C.$(y-p{)}^2=4qx$
   4. D.$(x-p{)}^2=4qy$
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   Answer: D