. Algebraic geometry; a new treatise on analytical conic sections . Squaring and multiplying up, we have But (x, y) is any point on either tangent. .. this is the equation of the two tangents OQ, OQ. *247. If PCP, DCD are conjugate diameters, and QQ a chordto DD cuts PP a* V, ^ CP2Take CP, CD as axes of co-ordinates, and let CP = a, CD = 6. Then —75 + t^j = ^ ^® *^® equation of the , being parallel to CD, is bisected by CP at Fio. 148. Let ia cos &, V sin ff) be the co-ordinates of Q. QV2 QV2 V^WCiW J2gin2^ Then CP^-CV^ a^-a^oosW a!-isai^6 ^cpg CP? Exs. X. g.]
. Algebraic geometry; a new treatise on analytical conic sections . Squaring and multiplying up, we have But (x, y) is any point on either tangent. .. this is the equation of the two tangents OQ, OQ. *247. If PCP, DCD are conjugate diameters, and QQ a chordto DD cuts PP a* V, ^ CP2Take CP, CD as axes of co-ordinates, and let CP = a, CD = 6. Then —75 + t^j = ^ ^® *^® equation of the , being parallel to CD, is bisected by CP at Fio. 148. Let ia cos &, V sin ff) be the co-ordinates of Q. QV2 QV2 V^WCiW J2gin2^ Then CP^-CV^ a^-a^oosW a!-isai^6 ^cpg CP? Exs. X. g.] PEOPEETIES OF THE ELLIPSE. 225 Examples X. g, 1. Draw the ellipse whose axes are 6 inches and 4 inches long. Findits foci, and measure their distances from the centre. Verify your meas-urements by calculation. 2. If a focal chord of an ellipse meets the auxiliary circle at Q and that SQ . SQ = BC^. 3. Prove that the acute angle between two conjugate diameters of anellipse is a minimum when they are equal. 4. If the diameter conjugate to the semi-diameter CP of an ellipseout the focal distances of P in the points L, M, then PL=PIV1. 5. Find the co-ordinates of the intersection of tangents to the ellipsera + p=l St the points whpse eccentric angles are B + a, 0-a, and if a isconstant deduce the fact that their tangents meet on the ellipse =« , y _i a^ sec^a 6^ seo^a 6. Given the axes ACA, BOB of an ellipse, and PP which is kno
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Keywords: ., bookcentury1900, bookdecade1910, bookpublisherlondo, bookyear1916
