1

### IIT-JEE 1984

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
2

### IIT-JEE 1983

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
3

### IIT-JEE 1983

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 1980

Two circles $${x^2} + {y^2} = 6$$ and $${x^2} + {y^2} - 6x + 8 = 0$$ are given. Then the equation of the circle through their points of intersection and the point (1, 1) is
A
$${x^2} + {y^2} - 6x + 4 = 0$$
B
$${x^2} + {y^2} - 3x + 1 = 0$$
C
$${x^2} + {y^2} - 4y + 2 = 0$$
D
none of these

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