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1

IIT-JEE 1987

Subjective
Let a given line $$L_1$$ intersects the x and y axes at P and Q, respectively. Let another line $$L_2$$, perpendicular to $$L_1$$, cut the x and y axes at R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.

solve it
2

IIT-JEE 1987

Subjective
The circle $${x^2}\, + \,{y^2} - \,4x\, - 4y + \,4 = 0$$ is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circumcentre of the triangle is $$x\, + \,y\, - xy\, + k\,{\left( {{x^2}\, + \,{y^2}} \right)^{1/2}} = 0$$. Find k.

k = 1
3

IIT-JEE 1986

Subjective
Lines 5x + 12y - 10 = 0 and 5x - 12y - 40 = 0 touch a circle $$C_1$$ of diameter 6. If the centre of $$C_1$$ lies in the first quadrant, find the equation of the circle $$C_2$$ which is concentric with $$C_1$$ and cuts intercepts of length 8 on these lines.

$${x^2}\, + \,{y^2} - \,10x\, - 4y + \,4 = 0\,$$
4

IIT-JEE 1984

Subjective
The abscissa of the two points A and B are the roots of the equation $${x^2}\, + \,2ax\, - {b^2} = 0$$ and their ordinates are the roots of the equation $${x^2}\, + \,2px\, - {q^2} = 0$$. Find the equation and the radius of the circle with AB as diameter.

$${x^2}\, + \,{y^2} + \,2ax\, + 2py\, - {b^2}\, - {q^2} = 0,\,\,\,\sqrt {{a^2}\, + \,{p^2} + {b^2}\, + \,{q^2}}$$

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