What are the steps for using a compass and straightedge to construct the bisector of ∠G? Two rays share a common endpoint labele
d G, forming an obtuse angle. One ray is horizontal and points right. The second ray is inclined to horizontal in upward-left direction. Drag the steps and drop them in order from start to finish. Without changing the opening of the compass, place the point of the compass on point J and draw another arc in the interior of the angle.Use the straightedge to draw GK−→−.Place the point of the compass on point H and draw an arc in the interior of the angle.Label the intersection of the arcs in the interior of the angle as point K.Place the point of the compass on point G and draw an arc that intersects the sides of ∠G. Label the points of intersection as points H and J.
2 answers:
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Solution:
Given:
Part A:
The vertex of an up-down facing parabola of the form;
Rewriting the equation given;
Therefore, the vertex is (0,0)
Part B:
A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)
Using the standard equation of a parabola;
Rewriting the equation in standard form,
Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)
Hence,
Therefore, the focus is;
Part C:
A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)
Using the standard equation of a parabola;
Rewriting the equation in standard form,
Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).
Hence,
Therefore, the directrix is;