Circle

$x+2y+5=0$

$x-2y-5=0$

$x+2y-5=0$

$x-2y+5=0$

60$^\circ$

30$^\circ$

45$^\circ$

90$^\circ$

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

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

$x^{2}+y^{2}+3x+4y=0$

$x^{2}+y^{2}-7x+7y=0$

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

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

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

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

(-1, -1), 2

(1, -1), 2

(-1, 1), 2

(1, 1), 2

$\left| C_{1}C_{2} \right|<\left| r_{2}-r_{1} \right|$

$\left| C_{1}C_{2} \right|>r_{2}+r_{1}$

$\left| r_{2}-r_{1} \right|<\left| C_{1}C_{2} \right|<r_{2}+r_{1}$

$\left| C_{1}C_{2} \right|>r_{2}\times r_{1}$

$\sqrt{2}$

$2\sqrt{2}$

$3\sqrt{2}$

$2\sqrt{3}$

4

20

-4

-20

$(0,2)$

$(2,0)$

$(1,0)$

$(-2,0)$

$x^{2}+y^{2}+8x+12y+47=0$

$x^{2}+y^{2}-8x-12y+47=0$

$x^{2}+y^{2}-8x+12y+47=0$

$x^{2}+y^{2}+8x-12y+47=0$

$x-2y=\pm 2\sqrt{5}$

$x-2y=\pm 2$

$x+2y=\pm 2\sqrt{3}$

$x+2y=\pm 2\sqrt{5}$

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

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

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

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

3

4

1

2

1

2

3

4

$x=\dfrac{a}{2}+\dfrac{\sqrt{a^{2}+b^{2}}}{2} \cos \theta, y=\dfrac{b}{2}+\dfrac{\sqrt{a^{2}+b^{2}}}{2} \sin \theta$

$x=\dfrac{-a}{2}+\dfrac{\sqrt{a^{2}+b^{2}}}{4} \sin \theta, y=\dfrac{-b}{2}+\dfrac{\sqrt{a^{2}+b^{2}}}{4} \cos \theta$

$x=\dfrac{a}{2}+\sqrt{\dfrac{a^{2}+b^{2}}{2}} \sin \theta, y=\dfrac{b}{2}+\sqrt{\dfrac{a^{2}+b^{2}}{2}} \cos \theta$

$x=\dfrac{a}{2}+\dfrac{\sqrt{a^{2}+b^{2}}}{4} \cos \theta, y=\dfrac{b}{2}+\dfrac{\sqrt{a^{2}+b^{2}}}{4} \sin \theta$