Circles, Ellipses, Conic Sections — Quiz 5

Questions in this quiz (10)

1. The equation of a circle is $$x^2 + (y+6)^2 = 16$$.What is the area of the circle's region that lies in Quadrant 1 of the $$xy$$-plane?

   • 6
   • 36
   • 16
   • 0

2. Which of the following equations represents a circle in the $$xy$$-plane that intersects the $$y$$-axis at exactly one point?

   • $$(x - 4)^2 + (y - 5)^2 = 25$$
   • $$(x - 4)^2 + (y - 10)^2 = 49$$
   • $$(x - 4)^2 + (y - 7)^2 = 9$$
   • $$x^2 + (y - 5)^2 = 25$$

3. If a circle with radius $$r$$ is divided into $$n$$ congruent arcs, what is the measure of each arc's length in terms of $$r$$ and $$n$$?

   • $$\frac{2\pi r}{n}$$
   • $$\frac{\pi r}{n}$$
   • $$\frac{r}{2\pi n}$$
   • $$\frac{4\pi r}{n}$$

4. What is the largest circle that can be inscribed in the ellipse given by the equation: $$\frac{(x - 3)^2}{16} + \frac{(y + 1)^2}{36} = 1$$

   • $$4\pi$$
   • $$3\pi$$
   • $$16\pi$$
   • $$9\pi$$

5. Which of these is the equation of the tangent to the circle $$(x + 3)^2 + (y - 2)^2 = 45 $$ at the point $$ (-1, 5)$$?

   • $$-\frac{2}{3}x + 13$$
   • $$\frac{1}{3}x + \frac{13}{3}$$
   • $$-\frac{2}{3}x + \frac{13}{3}$$
   • $$-\frac{1}{3}x + 5$$

6. Determine the type of conic represented by the equation:$$x^2 + 4x + 2y + 7 = 0$$

   • Circle
   • Ellipse
   • Parabola
   • Hyperbola

7. Determine the type of conic represented by the equation:$$\frac{x - 4}{y + 2} = \frac{y - 1}{x + 3}$$

   • Circle
   • Hyperbola
   • Parabola
   • Ellipse

8. An ellipse with a major axis of length 8 inches and a minor axis of length 6 inches is inscribed in a rectangle. The region inside the rectangle but outside the ellipse is shaded. What is the area, in square inches, of the shaded region?(Note: The area, $$A$$, of any ellipse can be found by the formula $$A = \pi ab$$, where $$a$$ is half the length of the major axis and $$b$$ is half the length of the minor axis.)

   • $$48 - 24\pi$$
   • $$48 - 12\pi$$
   • $$48 + 12\pi$$
   • $$48 + 24\pi$$

9. In a circle, the measure of the central angle $$\theta$$ is $$100^\circ$$. The length of the arc intercepted by this angle is $$15\pi$$ units. What is the radius of the circle?

   • $$15$$
   • $$15\pi$$
   • $$27$$
   • $$18\pi$$

10. In the standard $$(x,y)$$ coordinate plane, what is an equation of a circle that has center $$(-4,-2)$$ and is tangent to the $$x$$-axis?

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