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1

### IIT-JEE 1986

Fill in the Blanks
From the point A(0, 3) on the circle $${x^2} + 4x + {(y - 3)^2} = 0$$, a chord AB is drawn and extended to a point M such that AM = 2AB. The equation of the locus of M is..........................

$${x^2} + {y^2} + 8x - 6y + 9 = 0$$
2

### IIT-JEE 1985

Fill in the Blanks
Let $${x^2} + {y^2} - 4x - 2y - 11 = 0$$ be a circle. A pair of tangentas from the point (4, 5) with a pair of radi from a quadrilateral of area............................

8 sq unit
3

### IIT-JEE 1985

Fill in the Blanks
From the origin chords are drawn to the circle $${(x - 1)^2} + {y^2} = 1$$. The equation of the locus of the mid-points of these chords is.............

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

### IIT-JEE 1984

Fill in the Blanks
The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. The radius of this circle is ........................................

$$\,{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}$$

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