1.
Item 3. State the coordinates of the centre for the following conic: \((x+1)^2-4(y-3)^2=-36\).
Solution: Write in standard form. The center is read directly from \((x-h)^2\) and \((y-k)^2\). Since \((x+1)^2=(x-(-1))^2\) and \((y-3)^2\), the center is \((-1,3)\). Answer: C
2.
Item 2. State the radius for the following circle: \(x^2+y^2=16\).
Solution: The standard form is \(x^2+y^2=r^2\). Here \(r^2=16\), so \(r=\sqrt{16}=4\). Answer: C
3.
Item 1. From the following diagram identify the conic formed:
Solution: The plane is parallel to the side of the cone, producing a parabola. Therefore the conic formed is a parabola. Answer: D
4.
Item 4. What is the equation of the following parabola?
Solution: The parabola opens to the right, so its horizontal-axis form is \((y-k)^2=4a(x-h)\). The vertex is \((2,3)\). Therefore the equation is \((y-3)^2=4a(x-2)\). Answer: D
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