Plane and solid analytic geometry; an elementary textbook . Fig. 87. determined by finding the intersections of tangents atthe extremities of chords through the point. 2. The polar of any point P1 with respect to a centralconic is parallel to the tangent at the point where the diameterthrough P1 cuts the conic. Y. Fig. 88. Ch. XII, § 86] POLES AND POLARS 161 Let the coordinates of the point P2 where CP1 cuts thehyperbola be (xv ya). Then the equation of the tangent 2 k b2x2x — a2y2y = a2b2, and the equation of the polar of Px isb2xxx — a2yxy = a2b2. But since Px and P2 are on the same line thr
Plane and solid analytic geometry; an elementary textbook . Fig. 87. determined by finding the intersections of tangents atthe extremities of chords through the point. 2. The polar of any point P1 with respect to a centralconic is parallel to the tangent at the point where the diameterthrough P1 cuts the conic. Y. Fig. 88. Ch. XII, § 86] POLES AND POLARS 161 Let the coordinates of the point P2 where CP1 cuts thehyperbola be (xv ya). Then the equation of the tangent 2 k b2x2x — a2y2y = a2b2, and the equation of the polar of Px isb2xxx — a2yxy = a2b2. But since Px and P2 are on the same line through the x xorigin, — = —-, and these lines are evidently parallel. Let the student prove the same theorem for the ellipse. 3. The polar of any point Px with respect to a parabola isparallel to the tangent at the point where a diameter throughP1 cuts the parabola. Y
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