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1

### 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
2

### 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
3

### IIT-JEE 1980

A square is inscribed in the circle $${x^2} + {y^2} - 2x + 4y + 3 = 0$$. Its sides are parallel to the coordinate axes. The one vertex of the square is
A
$$\left( {1 + \sqrt {2,} - 2} \right)$$
B
$$\,\left( {1 - \sqrt {2}, - 2} \right)$$
C
$$\,\,\left( {1, - 2 + \sqrt 2 } \right)$$
D
none of these

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