1
IIT-JEE 1984
Subjective
+4
-0
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.
2
IIT-JEE 1983
Subjective
+5
-0
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 $$\,{x^2}\, + \,{y^2}$$ = $$hx + ky$$.
3
IIT-JEE 1981
Subjective
+4
-0
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.
4
IIT-JEE 1981
Subjective
+3
-0
Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.
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