Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
[tex]|PA|=\sqrt{(1-x)^2+(-2-y)^2}\\\\|PB|=\sqrt{(4-x)^2+(-3-y)^2}\\\\|PA|=2|PB|\\\\\sqrt{(1-x)^2+(-2-y)^2}=2\sqrt{(4-x)^2+(-3-y)^2}\\\\(1-x)^2+(-2-y)^2=4[(4-x)^2+(-3-y)^2]\\\\1-2x+x^2+4+4y+y^2=4(16-8x+x^2+9+6y+y^2)[/tex]
[tex]x^2+y^2-2x+4y+5=4(x^2+y^2-8x+6y+25)\\\\x^2+y^2-2x+4y+5=4x^2+4y^2-32x+24y+100\\\\x^2-4x^2-2x+32x+y^2-4y^2+4y-24y+5-100=0\\\\-3x^2+30x-3y^2-20y-95=0\ \ \ \ /:(-3)\\\\x^2-10x+y^2+\frac{20}{3}y+\frac{95}{3}=0\\\\x^2-2x\cdot5+5^2-5^2+y^2+2y\cdot\frac{10}{3}+\left(\frac{10}{3}\right)^2-\left(\frac{10}{3}\right)^2=-\frac{95}{3}[/tex]
[tex](x-5)^2+(y+\frac{10}{3})^2=-\frac{95}{3}+\frac{100}{9}+25\\\\(x-5)^2+(y+\frac{10}{3})^2=-\frac{285}{9}+\frac{100}{9}+\frac{225}{9}\\\\(x-5)^2+(y+\frac{10}{3})^2=\frac{40}{9}\\\\it's\ the\ circle\\\\center:(5;-\frac{10}{3})\\\\radius:r=\sqrt\frac{40}{9}=\frac{\sqrt{4\cdot10}}{\sqrt9}=\frac{2\sqrt{10}}{3}[/tex]
[tex]x^2+y^2-2x+4y+5=4(x^2+y^2-8x+6y+25)\\\\x^2+y^2-2x+4y+5=4x^2+4y^2-32x+24y+100\\\\x^2-4x^2-2x+32x+y^2-4y^2+4y-24y+5-100=0\\\\-3x^2+30x-3y^2-20y-95=0\ \ \ \ /:(-3)\\\\x^2-10x+y^2+\frac{20}{3}y+\frac{95}{3}=0\\\\x^2-2x\cdot5+5^2-5^2+y^2+2y\cdot\frac{10}{3}+\left(\frac{10}{3}\right)^2-\left(\frac{10}{3}\right)^2=-\frac{95}{3}[/tex]
[tex](x-5)^2+(y+\frac{10}{3})^2=-\frac{95}{3}+\frac{100}{9}+25\\\\(x-5)^2+(y+\frac{10}{3})^2=-\frac{285}{9}+\frac{100}{9}+\frac{225}{9}\\\\(x-5)^2+(y+\frac{10}{3})^2=\frac{40}{9}\\\\it's\ the\ circle\\\\center:(5;-\frac{10}{3})\\\\radius:r=\sqrt\frac{40}{9}=\frac{\sqrt{4\cdot10}}{\sqrt9}=\frac{2\sqrt{10}}{3}[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.