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Odd Extension of a Function

The equation ...

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The equation of common †an gents to the circles x2+y2-2x-6y+9=0 and x2+y2+6x-2y+1=0 is/ar 1. x=0 2. y -4=0 3. 3x+4y=10 4. 4x-3y=0

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Q. I : The equations to the direct common tangents to the circles

x^{2} + y^{2} + 6 x + 4 y + 4 = 0

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

y - 1 = 0

4 x - 3 y - 9 = 0

II : The equations to the transverse common tangents to the circles

x^{2} + y^{2} - 4 x - 10 y + 28 = 0

x^{2} + y^{2} + 4 x - 6 y + 4 = 0

x - 1 = 0, 3 x + 4 y - 21 = 0

Q. The internal common tangents of the circles

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

x^{2} + y^{2} + 6 x + 6 y + 9 = 0

Q. Find the radical centre of the three circles

x^{2} + y^{2} - 4 x - 6 y + 5 = 0

x^{2} + y^{2} - 2 x - 4 y - 1 = 0

x^{2} + y^{2} - 6 x - 2 y = 0

Q. The number of common tangents to the circles

x^{2} + y^{2} - 4 x - 2 y + 1 = 0

x^{2} + y^{2} - 6 x - 4 y + 4 = 0

Circles	Number of common tangents
I: $x^{2} + y^{2} = 4$ $x^{2} + y^{2} - 8 x + 12 = 0$	a) $0$
II: $x^{2} + y^{2} = 1$ $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$	b) $1$
III: $x^{2} + y^{2} = 16$ $x^{2} + y^{2} - 8 x + 6 y - 56 = 0$	c) $4$
IV: $x^{2} + y^{2} - 2 x - 6 y + 9 = 0$ $x^{2} + y^{2} + 6 x - 2 y + 1 = 0$	d) $3$

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