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1. What is the distance between the center of the circle with equation $$x^2+y^2=-4x+6y-12$$ and the point $$(1,7)$$?

2. The graph of the parabola $$x = 2y^2 - 6y + 3$$ has an x-intercept (a, 0) and two y-intercepts (0, b) and (0, c). Find a+b+c.

3. The line $$x = 4$$ is an axis of symmetry of the graph of  $$y = ax^2 + bx + c$$. Find $$\frac{b}{a}$$.

4. The graph of $$y = ax^2 + bx + c$$ is shown below. Find $$a \cdot b \cdot c$$. (The distance between the grid lines is one unit.) 5. Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola.

Suppose $$\mathcal{P}$$ is a parabola with focus (4, 3) and directrix y = 1. The point (8, 6) is on $$\mathcal{P}$$ because (8, 6) is 5 units away from both the focus and the directrix.

If we write the equation whose graph is $$\mathcal{P}$$ in the form $$y=ax^2 + bx + c$$, then what is $$a+b+c$$?

Does anyone know how to do any of these? (Possibly all?) Please also include an explanation if you can, thank you!

Jul 22, 2020