Circles, Ellipses, Conic Sections — Quiz 1

Questions in this quiz (6)

1. Which of these is the equation of an ellipse with:- Vertices $$(a,0)$$ and $$(-a,0)$$- Co-vertices $$(0,b)$$ and $$(0,-b)$$, where $$a^2 = 49$$ and $$b^2 = 36$$?

   • $$\frac{x^2}{36} + \frac{y^2}{49} = 1$$
   • $$\frac{x^2}{25} + \frac{y^2}{36} = 1$$
   • $$\frac{x^2}{49} + \frac{y^2}{36} = 1$$
   • $$\frac{x^2}{49} + \frac{y^2}{25} = 1$$

2. About 35% of the books that Liam owns are science fiction. If he were to construct a circle graph of his book collection, what would be the size (in degrees) of the central angle representing science fiction books?

   • $$120$$
   • $$126$$
   • $$110$$
   • $$130$$

3. About 25% of the apps on Noah's phone are educational. If he were to construct a circle graph of his apps using a circle with a radius of 2 inches, what would be the length of the arc of the portion of the circle representing educational apps?

   • $$\pi$$
   • $$0.5\pi$$
   • $$0.25\pi$$
   • $$2\pi$$

4. A circle graph is to be constructed from the data below. What is the size (in degrees) of the angle representing art majors?

   • 28.8
   • 25.7
   • 31.6
   • 22.7

5. In which quadrant of the xy-coordinate plane will you find the graph of the circle with the equation $$(x - 4)^2 + (y + 5)^2 = 9$$?

   • III
   • II
   • I
   • IV

6. In the $$xy$$-coordinate plane, a circle has a center at $$(-2,5)$$ and a radius of $$4$$. Which of these represents an equation of this circle?

   • $$(x - 2)^2 + (y - 5)^2 = 4$$
   • $$(x + 2)^2 + (y - 5)^2 = 4$$
   • $$(x + 2)^2 + (y - 5)^2 = 16$$
   • $$(x - 2)^2 + (y - 5)^2 = 16$$