1
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
$${x^2}\, + \,{y^2}\, - \,2\,\,ax\, - \,4\,by\, + \,\,({a^2}\, - \,\,{b^2}\, - \,\,{k^2})\, = \,0$$.
2
IIT-JEE 1984
+2
-0.5
The locus of the mid-point of a chord of the circle $${x^2} + {y^2} = 4$$ which subtends a right angle at the origin is
A
x + y = 2
B
$${x^2} + {y^2} = 1$$
C
$${x^2} + {y^2} = 2$$
D
$$x + y$$=1
3
IIT-JEE 1983
+1
-0.25
The centre of the circle passing through the point (0, 1) and touching the curve $$\,y = {x^2}$$ at (2, 4) is
A
$$\left( {{{ - 16} \over 5},{{ - 27} \over {10}}} \right)$$
B
$$\left( {{{ - 16} \over 7},{{53} \over {10}}} \right)$$
C
$$\left( {{{ - 16} \over 5},{{53} \over {10}}} \right)$$
D
none of these
4
IIT-JEE 1983
+1
-0.25
The equation of the circle passing through (1, 1) and the points of intersection of $${x^2} + {y^2} + 13x - 3y = 0$$ and $$2{x^2} + 2{y^2} + 4x - 7y - 25 = 0$$ is
A
$$4{x^2} + 4{y^2} - 30x - 10y - 25 = 0$$
B
$$4{x^2} + 4{y^2} + 30x - 13y - 25 = 0$$
C
$$4{x^2} + 4{y^2} - 17x - 10y + 25 = 0$$
D
none of these
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