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1

IIT-JEE 1993

Fill in the Blanks
The equation of the locus of the mid-points of the circle $$4{x^2} + 4{y^2} - 12x + 4y + 1 = 0$$ that subtend an angle of $$2\pi /3$$ at its centre is.................................

Answer

$$16{x^2} + 16{y^2} - 48x + 16y + 31 = 0$$
2

IIT-JEE 1991

Fill in the Blanks
If a circle passes through the points of intersection of the coordinate axes with the lines $$\lambda \,x - y + 1 = 0$$ and x - 2y + 3 = 0, then the value of $$\lambda $$ = .........

Answer

2
3

IIT-JEE 1989

Fill in the Blanks
The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $${x^2} + {y^2} = 4\,\,at\,\,\left( {1,\sqrt 3 } \right)$$ is,..................

Answer

$${2\sqrt 3 }$$ sq unit
4

IIT-JEE 1988

Fill in the Blanks
If the circle $${C_1}:{x^2} + {y^2} = 16$$ intersects another circle $${C_2}$$ of radius 5 in such a manner that common chord is of maximum lenght and has a slope equal to 3/4, then the coordinates of the centre of $${C_2}$$ are.............................

Answer

$$\,\left( { - {9 \over 5},{{12} \over 5}} \right)\,\,or\,\left( {{9 \over 5},\, - {{12} \over 5}} \right)$$

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