Focal chord
Web(iii) If l 1 and l 2 are the length of the focal segments, then length of the latusrectum = 2 (harmonic mean of focal segment) i.e., (iv) For a chord joining points P(at 1 2, 2at 1) and Q(at 2 2 , 2at 2) and passing through focus, then t 1 t 2 = 1. (v) Length of the focal chord having t 1 and t 2 as end points is a (t 1 — t 1) 2. WebFeb 3, 2024 · If a chord is drawn parallel to that focal chord which passes through vertex of parabola at (0,0) , it's length comes out to be 4 a c o s e c 2 θ c o s θ , it's quite easy to prove this using parametric coordinates for the parabola , I'm looking for an intuitive geometric demonstration that AB=A′B′.The equality certainly holds but I feel there …
Focal chord
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WebThe latus rectum of a parabola can also be understood as the focal chord which is parallel to the directrix of the parabola. The length of the latus rectum for a standard equation of … WebNov 20, 2024 · Let P denote the point (8,8) on the parabola x^2=8y and let PQ be a focal chord.A) find the coordinates of QB) find the length of PQC) find the equation of the circle with this focal chord as a diameter.D) show that this circle intersects the directrix of the parabola in only one point. Conclude that the directrix is tangent to the circle.
WebNov 14, 2024 · focal: [adjective] of, relating to, being, or having a focus. WebFocal Chord: The focal chord of a parabola is the chord passing through the focus of the parabola. The focal chord cuts the parabola at two distinct points. Focal Distance: The distance of a point (x1,y1) ( x 1, y 1) on the parabola, from the focus, is the focal distance.
WebApr 7, 2024 · Complete step-by-step answer: Any chord to y 2 = 4 a x which passes through the focus is called a focal chord of the parabola y 2 = 4 a x. Focus can be defined as a point in parabola with coordinates ( a, 0). Consider a point P on the parabola whose coordinate in parametric form be ( a t 2, 2 a t). WebNov 20, 2013 · 3 Answers. Sorted by: 5. This is the length of the focal chord (the "width" of a parabola at focal level). Let x 2 = 4 p y be a parabola. Then F ( 0, p) is the focus. Consider the line that passes through the focus and parallel to the directrix. Let A and A ′ be the intersections of the line and the parabola. Then A ( − 2 p, p), A ′ ( 2 p ...
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