1

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
2

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

$$\,\left( { - {9 \over 5},{{12} \over 5}} \right)\,\,or\,\left( {{9 \over 5},\, - {{12} \over 5}} \right)$$
3

IIT-JEE 1987

Fill in the Blanks
The area of the triangle formed by the tangents from the point (4, 3) to the circle $${x^2} + {y^2} = 9$$ and the line joining their points of contact is...................

Answer

$${{192} \over {25}}$$
4

IIT-JEE 1986

Fill in the Blanks
The equation of the line passing through the points of intersection of the circles $$3{x^2} + 3{y^2} - 2x + 12y - 9 = 0$$ and $${x^2} + {y^2} - 6x + 2y - 15 = 0$$ is..............................

Answer

10x - 3y - 18 = 0

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