| Norman Macleod Ferrers - 1861 - 166 páginas
...one of which is the line at infinity; and. the other must represent the directrix, since that is the **locus of the point of intersection of two tangents to a parabola** at right angles to one another. The appearance of the line at infinity as a factor in the result in... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880
...angles. 13. Find the condition that the line, у = mx -\- c, may be a tangent to the parabola, y' = iax. **Find the locus of the point of intersection of two tangents to a parabola, which are** inclined to each other at an angle of 45°. 14. Trace the curve represented by the equation y* - Щ... | |
| Edward Albert Bowser - 1880 - 287 páginas
...(2)], 6 vv I/ = -- ; X -- . . (5) aey y . v' which is perpendicular to (4), by Art. 27, Cor. 1. 127. **Find the locus of the point of intersection of two tangents to** an hyperbola at right angles to each other. Reason as in Art. 94, or change V* into — A2 in equation... | |
| Charles Smith - 1883 - 352 páginas
...point Q, then will the polar of Q pass through P. This may be proved exactly as in Art. 78. ' 1 20. **To find the locus of the point of intersection of two tangents to** an ellipse which are at right angles to one another. The line whose equation is y = mx + JaV + b'1... | |
| Charles Smith - 1883 - 352 páginas
...meet the directrix in M, shew that MQ will be parallel to the axis of the parabola. 4. Shew that the **locus of the point of intersection of two tangents to a parabola** at points on the curve whose ordinates are in a constant ratio is a parabola. 5. The two tangents from... | |
| Charles Smith - 1894 - 352 páginas
...is a normal to the curve. 107. We shall conclude this Chapter by the solution of some examples. (1) **To find the locus of the point of intersection of two tangents to a parabola which** make a given angle with one another. The line y = mx + - is a tangent to the parabola y* - 4<za; =... | |
| Luigi Cremona - 1885 - 302 páginas
...HK, and lying at the same distance from HK (on the opposite side) that F does. That is to say : The **locus of the point of intersection of two tangents to a parabola which** cut at right angles is the directrix*. Since the director circle of a conic is concentric with the... | |
| 1893
...e and /> signify respectively the eccentricity and half the latus rectum of the inverted conic. The **locus of the point of intersection of two tangents to a parabola which** cut one another at a constant angle is a hyperbola having the same focus and directrix as the original... | |
| ASUTOSH MUHKOPADHYAY - 1893
...perpendicular to the directrix and SP; then 0/-/SJ7(Chap. L, Prop. XIII.), and Ex. 10. Prove that the **locus of the point of intersection of two tangents to a parabola which** cut at a constant angle is a hyperbola, which is a constant ratio greater than unity since L.OSP—Tr... | |
| 1893
...e and / signify respectively the eccentricity and half the latus rectum of the inverted conic. The **locus of the point of intersection of two tangents to a parabola which** cut one another at a constant angle is a hyperbola having the same focus and directrix as the original... | |
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