1

### IIT-JEE 1993

Subjective
Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that the chords on which the circle $${x^2}\, + \,{y^2} - \,4x - \,6y - 3 = 0$$ cuts the members of the family are concurrent at a point. Find the coordinate of this point.

$$\left( {2\,,{{23} \over 3}} \right)$$
2

### IIT-JEE 1993

Subjective
Find the coordinates of the point at which the circles $${x^2}\, + \,{y^2} - \,4x - \,2y = - 4\,\,and\,\,{x^2}\, + \,{y^2} - \,12x - \,8y = - 36$$ touch each other. Also find equations common tangests touching the circles in the distinct points.

$$\left( {{{14} \over 5},{8 \over 5}} \right),\,\,y = 0$$ and $$7y - \,24x\, + \,16\, = 0$$
3

### IIT-JEE 1992

Subjective
Let a circle be given by 2x (x - a) + y (2y - b) = 0, $$(a\, \ne \,0,\,\,b\, \ne 0)$$. Find the condition on a abd b if two chords, each bisected by the x-axis, can be drawn to the circle from $$\left( {a,\,\,{b \over 2}} \right)$$.

$${a^2}\, > \,2\,{b^2}$$
4

### IIT-JEE 1991

Subjective
Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangent is 4x + 3y = 10, find the equation of the circles.

$${x^2}\, + \,{y^2} + 6x\, + 2y - 15\, = 0$$ and
$${x^2}\, + \,{y^2} - 10x\, - 10y + 25\, = 0$$

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