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1

### IIT-JEE 1985

Fill in the Blanks
From the origin chords are drawn to the circle $${(x - 1)^2} + {y^2} = 1$$. The equation of the locus of the mid-points of these chords is.............

$${x^2} + {y^2} - x = 0$$
2

### IIT-JEE 1984

Fill in the Blanks
The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. The radius of this circle is ........................................

$$\,{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}$$
3

### IIT-JEE 1983

Fill in the Blanks
The point of intersection of the line 4x - 3y - 10 = 0 and the circle $${x^2} + {y^2} - 2x + 4y - 20 = 0$$ are ........................and ...................

(4, 2), (- 2, - 6)
4

### IIT-JEE 1982

Fill in the Blanks
If A and B are points in the plane such that PA/PB = k (constant) for all P on a given circle, then the value of k cannot be equal to ..........................................

1

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