Circles, Ellipses, Conic Sections — Quiz 4

Questions in this quiz (7)

1. A circle in the $$xy$$-plane has a center at $$(7,10)$$. A point $$(7,18)$$ lies on the circle. Which of the following equations represents the circle?

   • $$(x-10)^2 + (y-7)^2 = 8$$
   • $$(x+7)^2 + (y+10)^2 = 8$$
   • $$(x-7)^2 + (y-10)^2 = 64$$
   • $$(x-10)^2 + (y-7)^2 = 64$$

2. If a circle is tangent to the x-axis at $$x = -4$$ and is tangent to the y-axis at $$y = 4$$, what is the equation of the circle?

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

3. For a school event, students are designing party hats shaped like cones. If each hat has a radius of 2 inches, what is the range of possible heights, $$h$$, if the volume of each hat must be between $$4\pi$$ and $$8\pi$$ cubic inches?

   • $$1$$ < $$h$$ < $$2$$
   • $$3$$ < $$h$$ < $$6$$
   • $$4$$ < $$h$$ < $$8$$
   • $$1$$ < $$h$$ < $$4$$

4. Write equations for the circles satisfying the conditions. The radius is 2. Lines $$x=-3$$ and $$y=4$$ each divide the circle into two half circles.

   • $$(x-3)^2+(y+4)^2=2$$
   • $$(x-3)^2+(y+4)^2=4$$
   • $$(x+3)^2+(y-4)^2=2$$
   • $$(x+3)^2+(y-4)^2=4$$

5. Point $$C(4,-1)$$ is on the circumference of a circle. Among all other points on the circumference, point $$D(-2,5)$$ is the farthest from $$C$$. Write the equation of the circle satisfying these conditions.

   • $$(x+1)^2+(y+2)^2=18$$
   • $$(x+1)^2+(y+2)^2=9$$
   • $$(x+1)^2+(y-2)^2=9$$
   • $$(x-1)^2+(y-2)^2=18$$

6. Find the x radius, y radius, foci, and center of $$x^2+9y^2+4x-18y=10$$

   • $$(-2-\frac{2\sqrt{46}}{3},-1)$$ and $$(-2-\frac{2\sqrt{46}}{3},-1)$$
   • $$(2-\frac{2\sqrt{46}}{3},1)$$ and $$(-2+\frac{2\sqrt{46}}{3},-1)$$
   • $$(-2+\frac{2\sqrt{46}}{3},1)$$ and $$(-2-\frac{2\sqrt{46}}{3},1)$$
   • $$(-2-\frac{2\sqrt{46}}{3},-1)$$ and $$(-2-\frac{2\sqrt{46}}{3},1)$$

7. Write an ellipse to satisfy each set of conditions. The center is at the origin. Its two axes are 12 and 6 units long, and the major axis is on the $$x$$-axis.

   • $$\frac{x^2}{36}+\frac{y^2}{9}=1$$
   • $$\frac{x^2}{6}+\frac{y^2}{3}=1$$
   • $$\frac{x^2}{6}+\frac{y^2}{3}=3$$
   • $$\frac{x^2}{6}+\frac{y^2}{9}=3$$