Practice Questions - Quantum ACT Prep

In the standard $(x, y)$ coordinate plane, the coordinates of the two ends of a diameter of a circle are $(3, -2)$ and $(-5, 6)$, respectively. What are the coordinates of the center of the circle?
1. $(-2, 1)$
2. $(-2, 2)$
3. $(-2, 4)$
4. $(-1, 2)$
5. $(-1, 4)$
In the standard $(x, y)$ plane, a circle has a center at $(2, -3)$ and a circumference of $8\pi$. Which of the following is an equation for this circle?
1. $(x-2)^2 + (y-3)^2 = 16$
2. $(x+2)^2 + (y-3)^2 = 16$
3. $(x-2)^2 + (y+3)^2 = 16$
4. $(x+2)^2 + (y-3)^2 = 64$
5. $(x-2)^2 + (y+3)^2 = 64$
What is the equation of a circle that has twice the radius and is concentric to the circle $x^2+4x+y^2-10y=7$?
1. $(x+2)^2+(y-5)^2=144$
2. $(x-2)^2+(y+5)^2=144$
3. $(x-2)^2+(y+5)^2=36$
4. $(x+2)^2+(y-5)^2=14$
5. $(x-2)^2+(y+5)^2=14$
Which of the following is the equation of a circle in the standard $(x, y)$ plane that has a radius of 3 units and is tangent to the $y-$axis at $(0, -1)$?
1. $x^2+y^2-3x+y-1=0$
2. $x^2+y^2+6x-2y-1=0$
3. $x^2+y^2-6x+2y+1=0$
4. $x^2+y^2+2y-8=0$
5. $x^2+y^2-2y+8=0$
What is the equation of a line that is tangent to the circle $(x-2)^2+(y-3)^2=25$ at the point where the circle intersects the positive $x-$axis?
1. $3x+4y=24$
2. $3x-4y=8$
3. $3x-4y=24$
4. $4x+3y=24$
5. $4x-3y=24$