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1

### IIT-JEE 1983

Subjective
Through a fixed point (h, k) secants are drawn to the circle $$\,{x^2}\, + \,{y^2} = \,{r^2}$$. Show that the locus of the mid-points of the secants intercepted by the circle is $$\,{x^2}\, + \,{y^2}$$ = $$hx + ky$$.

solve it
2

### IIT-JEE 1981

Subjective
Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.

$${x^2}\, + \,{y^2} + \,\,2\,\left( {10\,\, \pm \,\,\sqrt {54} } \right)\,x\, + \,\,55\,\, \pm \,\,\sqrt {54} = \,0$$
3

### IIT-JEE 1981

Subjective
Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$. Suppose that the tangents at the points B (1, 7) and D (4. - 2) on the circle meet at the point C. Find the area of the quadrilateral ABCD.

72 sq units
4

### IIT-JEE 1978

Subjective
Find the equation of the circle whose radius is 5 and which touches the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$ at the point (5, 5).

$${x^2}\, + \,{y^2}\, - \,18x\,\, - 16y\, + 120 = 0\,$$

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