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Length of Tangent and Power of a Point

1.The circle ...

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1.The circle to which two tangents can be drawn from origin is 1) x2+ y-8x-4y-3 0 2 ) x2 + y2 + 4x + 2y + 2 = 0 3 ) x2 + y2-8x + 6y + 1 = 0 4) both (2) &(3)

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Q. The number of common tangents that can be drawn to the circle

x^{2} + y^{2} - 4 x - 6 y - 3 = 0

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

Q. The number of common tangents that can be drawn to the circle

x^{2} + y^{2} - 4 x - 6 y - 3 = 0

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

is ___________.

Q. The angle between the circles

x^{2} + y^{2} - 4 x - 6 y - 3 = 0, x^{2} + y^{2} + 8 x - 4 y + 11 = 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) $3$

Q. The number of common tangents to the circles

x^{2} + y^{2} - 4 x - 6 y - 3 = 0

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

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