1.
Item 2. What is the equation of a circle with a center at \((0,0)\) and a radius of \(3\)?
Solution: The standard equation is \(x^2+y^2=r^2\). Since \(r=3\), \(r^2=9\). Therefore \(x^2+y^2=9\). Answer: A
2.
Item 3. State the coordinates of the center for the following conic: \((x+1)^2-4(y-3)^2=-36\).
Solution: From \((x-h)^2\) and \((y-k)^2\), the center is \((h,k)\). Here \(x+1=x-(-1)\) and \(y-3\), so the center is \((-1,3)\). Answer: B
3.
Item 1. From the following diagram identify the conic formed:
Solution: The plane is parallel to the base of the cone, producing a circular cross section. Therefore the conic formed is a circle. Answer: B
4.
Item 4. What is the equation of the following parabola?
Solution: The graph shows a parabola opening to the right with vertex \((-1,-2)\). A horizontal parabola has form \((y-k)^2=4a(x-h)\). Substituting the vertex gives \((y+2)^2=4a(x+1)\). Answer: C
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