 Prove that the ordinate of the point of intersection of two tangents to a parabola is the arithmetical mean between the ordinates of the points of contact of the tangents.  Analytic Geometry - Page 138by Lewis Parker Siceloff, George Wentworth, David Eugene Smith - 1922 - 290 pagesFull view - About this book
 | Electronic journals - 1902 - 232 pages
..."In the parabola y* = 4ax let/J, Q, It be points whose ordinates are in geometric progression : then the tangents at P and R meet on the ordinate of Q." Transforming by (A) we have : In the circle x* + y* = 4ax let P, (J, It be three points whose radii... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...P, Q, and E be three points on a parabola whose ordinates are in geometrical progression, prove that the tangents at P and R meet on the ordinate of Q. 22. Tangents are drawn to a parabola at points whose abscissa are in the ratio ft : 1 ; prove that... | |
 | William Meath Baker - Conic sections - 1906 - 363 pages
...If P, Q, R be three points on a parabola whose ordinates are in geometrical progression, prove that the tangents at P and R meet on the ordinate of Q. 27. The normal at P meets the parabola y^ — 4ax again at Q ; if x1 is the abscissa of P, prove that... | |
 | Henry Burchard Fine, Henry Dallas Thompson - Geometry, Analytic - 1909 - 346 pages
...P, Q, IÎ are three points on a parabola, whose ordinates are in geometrical progression, prove that the tangents at P and R meet on the ordinate of Q produced. 41. If r denote the distance of a point P on the parabola y2 = 4 ax from the focus, and p the perpendicular... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Mathematics - 1907 - 412 pages
...R are three points on a parabola, the ordinates of which are in geometrical progression, show that the tangents at P and R meet on the ordinate of Q. 69. Show that the tangents at the extremities of the latus rectum * of a parabola are perpendicular... | |
 | Frederick Shenstone Woods, Frederick Harold Bailey - Calculus - 1917 - 542 pages
...parabola, P, Q, and R are three points the ordinates of which are in geometrical progression, show that the tangents at P and R meet on the ordinate of Q. 78. Show that the tangents at the extremities of the chord of a parabola, which is perpendicular to... | |
 | Arthur McCracken Harding, George Walker Mullins - Geometry, Analytic - 1924 - 340 pages
...If P, Q, and R are three points on a parabola whose ordinates are in geometrical progression, then the tangents at P and R meet on the ordinate of Q. 8. If two straight lines VP and VQ are drawn through the vertex at right angles to one another, meeting... | |
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