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Parabola (magenta) and line (lower light blue) including a chord (blue). The area enclosed between them is in pink. The chord itself ends at the points where the line intersects the parabola. The area enclosed between a parabola and a chord (see diagram) is two-thirds of the area of a parallelogram that surrounds it.
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In this position, the hyperbolic paraboloid opens downward along the x-axis and upward along the y-axis (that is, the parabola in the plane x = 0 opens upward and the parabola in the plane y = 0 opens downward). Any paraboloid (elliptic or hyperbolic) is a translation surface, as it can be generated by a moving parabola directed by a second ...
If 0 < e < 1 the conic is an ellipse, if e = 1 the conic is a parabola, and if e > 1 the conic is a hyperbola. If the distance to the focus is fixed and the directrix is a line at infinity, so the eccentricity is zero, then the conic is a circle.
A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.
Israeli researchers found that hyperbaric oxygen therapy could improve PTSD in combat veterans. Dr. Marc Siegel discusses mental health in the military and how this treatment could help.
A viral post shared on X claims Florida Republican Rep. Matt Gaetz purportedly made a tweet about “age gap dating.” View on Threads Verdict: False The claim is false. The purported tweet was ...
In a parabola, the axis of symmetry is perpendicular to each of the latus rectum, the directrix, and the tangent line at the point where the axis intersects the parabola. From a point on the tangent line to a parabola's vertex, the other tangent line to the parabola is perpendicular to the line from that point through the parabola's focus.