Circles, Ellipses, Conic Sections — Quiz 2

Questions in this quiz (7)

1. If a $$120^\circ$$ arc on a circle measures $$10$$ inches, what is the circumference of this circle in inches?

   • 30
   • 120
   • 10
   • 40

2. Points $$A$$, $$B$$, and $$C$$ lie on a circle. A line drawn from $$A$$ to $$C$$ passes through the center of the circle. Which of the following is true about the measurement of the angle formed by points $$A$$, $$B$$, and $$C$$?

   • 90
   • 45
   • 180
   • 60

3. Point $$A$$ is outside circle $$O$$. How many distinct lines tangent to the circle can be drawn through point $$A$$?

   • 0
   • 1
   • 2
   • Infinite

4. How many points are necessary to determine a circle?

   • 1
   • 2
   • 3
   • Infinite

5. Find the radius r and the center O of the circle below:$$x^2 + y^2 = 1$$

   • $$O(0, 0)$$, $$r=1$$
   • $$O(1, 1)$$, $$r=1$$
   • $$O(-1, -1)$$, $$r=\sqrt{2}$$
   • $$O(0, 0)$$, $$r=\sqrt{2}$$

6. Write the ellipse $$4x^2+9y^2-8x+36y=91$$ in standard form.

   • $$\frac{(x+1)^2}{\frac{131}{9}}+\frac{(y-2)^2}{\frac{131}{9}}=1$$
   • $$\frac{(x-1)^2}{\frac{131}{4}}+\frac{(y+2)^2}{\frac{131}{9}}=1$$
   • $$\frac{(x-1)^2}{\frac{131}{9}}+\frac{(y+2)^2}{\frac{131}{9}}=1$$
   • $$\frac{(x-1)^2}{\frac{131}{9}}+\frac{(y-2)^2}{\frac{131}{4}}=1$$

7. Find the foci and center of the ellipse$$\frac{(x+2)^2}{25}+\frac{(y-3)^2}{36}=1$$

   • $$(2,3+\sqrt{11})$$ and $$(-2,-3-\sqrt{11})$$
   • $$(-2,-3+\sqrt{11})$$ and $$(2,3-\sqrt{11})$$
   • $$(-2,3+\sqrt{11})$$ and $$(-2,-3-\sqrt{11})$$
   • $$(-2,3+\sqrt{11})$$ and $$(-2,3-\sqrt{11})$$