1
IIT-JEE 1992
+2
-0.5
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle $${x^2} + {y^2} = 9$$is
A
$$\left( {{3 \over 2},{1 \over 2}} \right)\,$$
B
$$\left( {{1 \over 2},{3 \over 2}} \right)\,$$
C
$$\left( {{1 \over 2},{1 \over 2}} \right)\,$$
D
$$\left( {{1 \over 2}, - {2^{{1 \over 2}}}} \right)\,$$
2
IIT-JEE 1989
+2
-0.5
If the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$ intersect in two distinct points, then
A
2 < r < 8
B
r < 2
C
r = 2
D
r > 2
3
IIT-JEE 1989
+2
-0.5
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is
A
$${x^2} + {y^2} + 2x - 2y = 62$$
B
$${x^2} + {y^2} + 2x - 2y = 47$$
C
$${x^2} + {y^2} - 2x + 2y = 47$$
D
$${x^2} + {y^2} - 2x + 2y = 62$$c
4
IIT-JEE 1988
+1
-0.25
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2}\, = \,{k^2}$$ orthogonally, then the equation of the locus of its centre is
A
$$2\,ax\, + \,2\,by\, - \,({a^2}\, + \,{b^2}\, + \,\,{k^2})\, = \,0$$
B
$$2\,ax\, + \,2\,by\, - \,({a^2}\, - \,\,{b^2}\, + \,\,{k^2})\, = \,0$$
C
$${x^2}\, + \,{y^2}\, - \,3\,\,ax\, + \,4\,by\, + \,\,({a^2}\, + \,\,{b^2}\, - \,\,{k^2})\, = \,0$$
D
$${x^2}\, + \,{y^2}\, - \,2\,\,ax\, - \,4\,by\, + \,\,({a^2}\, - \,\,{b^2}\, - \,\,{k^2})\, = \,0$$.
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