. Plane and solid analytic geometry; an elementary textbook. —X 9 Fig. 88. Ch. XII, | POLES AND POLARS 161 Let the coordinates of the point P2 where CPX cuts thehyperbola be (xvy^). Then the equation of the tangent 2 b2x2x — a2y2y = a2b\ and the equation of the polar of P1 isb2xxx — a2yxy = since Px and P2 are on the same line through theorigin, -i = -?, and these lines are evidently the student prove the same theorem for the The polar of any point Px with respect to a parabola isparallel to the tangent at the point ivhere a diameter throughP1 cuts the parabola
. Plane and solid analytic geometry; an elementary textbook. —X 9 Fig. 88. Ch. XII, | POLES AND POLARS 161 Let the coordinates of the point P2 where CPX cuts thehyperbola be (xvy^). Then the equation of the tangent 2 b2x2x — a2y2y = a2b\ and the equation of the polar of P1 isb2xxx — a2yxy = since Px and P2 are on the same line through theorigin, -i = -?, and these lines are evidently the student prove the same theorem for the The polar of any point Px with respect to a parabola isparallel to the tangent at the point ivhere a diameter throughP1 cuts the parabola. Pi, Y /P2 /Ps \ y \° / Y Fig. 89. We may let the coordinates of P2 be (x2,y^). Thenthe equation of the tangent at P2 is yxy = mx + mx2, andthe equation of the polar of Px is yxy — mx + mxv Theseequations are seen at once to represent parallel lines. 162 ANALYTIC GEOMETRY [Ch. XII, § 86 These two theorems show that the polar of a point on adiameter is one of the system of parallel chords bisectedby that diameter. 4. If the line joining the centr
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