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Category Archive for: ‘Analytic Geometry’

How Do I Find the Focus of a Parabola?

This is a common question that we get from two audiences. It is most commonly asked by algebra students who want to calculate the point in the plane, when the equation of the parabola is given. More advanced students sometimes must prove this formula from the definition of the focus. We will handle this scenario second. We have also included …

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How Do I Know Which Direction the Parabola Opens?

From the Value of a There are a couple of ways we can determine the direction the parabola opens. The a-value is one way. If a > 0, then the parabola opens upward. If a < 0, then the parabola opens downward. Recall that when the parabola is given in standard form, y = ax¬≤ + bx + c, the …

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Finding the Directrix of a Parabola, Given its Vertex and Focus

Finding the directrix of a parabola, given its vertex and focus, when the equation of the parabola and its orientation are unknown.

Determining the Orientation of the Parabola Any time we are given only one or more of the following: Focus Vertex Axis of Symmetry Directrix and are asked to find one or more of the others, we must first determine the orientation of the parabola, if we are not already told what it is (as we usually are not). In the …

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