Circles, Ellipses, Conic Sections — Quiz 3

Questions in this quiz (8)

1. The endpoints of the diameter of a circle $$O$$ are $$A$$ and $$C$$. In the standard $$(x, y)$$ coordinate plane, $$A$$ is at $$(1, 2)$$ and $$C$$ is at $$(-5, -6)$$. What is the $$y$$-coordinate of the center of the circle?

   • -6
   • -4
   • -2
   • -5

2. Which of these is the equation of a circle with center $$(2\sqrt{3}, \sqrt{7}) $$ and radius $$ \sqrt{6}$$?

   • $$(x - 2\sqrt{3})^2 + (y - \sqrt{7})^2 = \sqrt{6}$$
   • $$(x - 2\sqrt{3})^2 + (y - \sqrt{7})^2 = 36$$
   • $$(x - 3)^2 + (y - 7)^2 = 6$$
   • $$(x - 2\sqrt{3})^2 + (y - \sqrt{7})^2 = 6$$

3. What is the positive $$y$$-coordinate of a point on the circle $$x^2 + y^2 = 16$$ with an $$x$$-coordinate of $$-3$$?

   • $$3$$
   • $$\sqrt{7}$$
   • $$7$$
   • $$\sqrt{3}$$

4. What are the $$x$$-intercepts of the circle $$ (x - 4)^2 + (y + 5)^2 = 64$$?

   • 5
   • $$-5 \pm \sqrt{39}$$
   • $$4 \pm \sqrt{39}$$
   • $$5 \pm \sqrt{39}$$

5. 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 $$b^2 = 36$$?

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

6. Which of these is the equation of an upward-facing parabola with vertex $$(3,4)$$ that passes through the point $$(6,10)$$?

   • $$y - 4 = (x - 3)^2$$
   • $$y - 4 = \frac{2}{3}(x - 3)^2$$
   • $$y - 4 = \frac{5}{6}(x - 3)^2$$
   • $$y - 4 = \frac{7}{10}(x - 3)^2$$

7. If the circle $$(x-4)^2+(y-5)^2=25$$ is moved up 2 and right 6 and the radius is doubled, what is the equation of the new circle?

   • $$(x-10)^2+(y-3)^2=50$$
   • $$(x+6)^2+(y+2)^2=200$$
   • $$(x-6)^2+(y+2)^2=100$$
   • $$(x-10)^2+(y-7)^2=100$$

8. A circle in the standard $$(x,y)$$ coordinate plane intersects the $$y$$-axis at $$(0,-4)$$ and $$(0,6)$$. The radius of the circle is $$5$$ coordinate units. Which of the following could be the center of the circle?I. $$(−3,1)$$II. $$(0,1)$$III. $$(3,1)$$

   • I, III
   • II only
   • I, II, III
   • III only