[math]x^2+10x+ \boxed{ }[/math]

[math]x^2-16x+\boxed{ }[/math] [br]

[math]x^2+40x+\boxed{ }[/math][br]

[math]x^2+5x+\boxed{ }[/math]

[size=150]Here is the equation of a circle: [math]x^2+y^2-6x-20y+105=0[/math][br][br]Elena wants to find the center and radius of the circle. Here is what she’s done so far.[br][br]Step 1: [math]x^2-6x+y^2-20y=-105[/math][br]Step 2: [math]x^2-6x+9+y^2-20y+100=-105+9+100[/math][br]Step 3: [math]x^2-6x+8+y^2-20y+100=4[/math][/size][br][br]What did Elena do in the first step?[br]

Why did Elena add 9 and 100 to the [i]left [/i]side of the equation in Step 2?[br]

Why did Elena add 9 and 100 to the [i]right [/i]side of the equation in Step 2?[br]

What should Elena do next?[br]

What are the center and radius of this circle?[br]

[size=150]Here is the equation of a circle: [math]x^2+y^2-2x+4y-4=0[/math][br][/size][br]Find the center and radius of the circle. Explain or show your reasoning.[br]

Triangulation is a process of using 3 distances from known landmarks to locate an exact position. Find a point that is located 5 units from the point [math]\left(3,4\right)[/math], 13 units from the point [math]\left(11,-4\right)[/math], and 17 units from the point [math]\left(21,16\right)[/math]. Use the coordinate grid if it’s helpful.