 | Sir Asutosh Mookerjee - Conic sections - 1893 - 197 pages
...given circle at P and Q. Construct a parabola which shall touch TP in P and have TQ for axis. Ex. 8. The locus of the foot of the perpendicular from the focus on the normal is a parabola. [Apply Prop. IV. SG is the axis, the vertex is at /S', the latus rectum— Ex.... | |
 | Sir Richard Glazebrook, Sir W. N. Shaw - Physics - 1893 - 668 pages
...The directrix is the locus of intersections of tangents at right angles, the tangent at the vertex is the locus of the foot of the perpendicular from the focus on the tangents, and thus each of these lines can be drawn when the curve1 only is figured on the paper. 1... | |
 | Education - 1897 - 680 pages
...angles to the directrix, PA produced meets the directrix in K ; show that HSK is a right angle. 3. Find the locus of the foot of the perpendicular from the focus on the tangent to the parabola. Two parabolas have the same focus S, and tangents are drawn to both parabolas at their... | |
 | 1898 - 870 pages
...locus of its centre. 3. Find the equations of the tangent and normal at any point of a parabola. Shew that the locus of the foot of the perpendicular from the focus on any normal to a parabola is a parabola. 4. Shew that the area of any parallelogram which touches an... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...isosceles triangle is formed by the focal distance of a point, the normal at the point and the axis. Find the locus of the foot of the perpendicular from the focus on the normal. (This question is to be solved geometrically.) 14. Prove that the feet of the perpendiculars... | |
 | University of Sydney - 1903 - 662 pages
...right angle. Prove that the other tangents to the conic through T, T' intersect on the directrix. 2. The locus of the foot of the perpendicular from the focus on a tangent to a parabola is the tangent at the vertex, and the length of the perpendicular is a mean... | |
 | Encyclopedias and dictionaries - 1907 - 794 pages
...be observed, is the tangent to the parabola at the vertex A. It appears, therefore, that the loons of the foot of the perpendicular from the focus on the tangent at any point is the tangent at the vertex. It oan also be seen that, if the tangent at P meet the axis... | |
 | Clement Vavasor Durell - Geometry, Plane - 1910 - 384 pages
...is constant. 144. Reciprocate wrt O : AB is a diameter of a circle AOPB ; then APB=<)o°. 145. Prove that the locus of the foot of the perpendicular from the focus of a parabola to a variable tangent is a straight line. 146. ABCD is a quadrilateral circumscribing... | |
 | Norman Colman Riggs - Geometry, Analytic - 1910 - 318 pages
...— b'2, if a > 6, but that there are no perpendicular tangents if a < 6. What if a = b '! 30. Prove that the locus of the foot of the perpendicular from the focus upon a tangent to 62x2 — aV2 = a2ft2 is the circle x2 + y'2 = a2. Check graphically. 31. Find the... | |
 | Norman Colman Riggs - Geometry, Analytic - 1911 - 330 pages
...— 6'2, if a > 6, but that there are no perpendicular tangents if a < 6. What if a = 6 ? 30. Prove that the locus of the foot of the perpendicular from the focus upon a tangent to 62x2 — a2?/'2 = a262 is the circle x2 + y2 = a2. Check graphically. 31. Find the... | |
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... the locus of the centres of circles described through the origin to touch the inverse curve. Thus from the theorem that the locus of the foot of the perpendicular from the focus on the tangent of a conic is a circle, we deduce (as Mr. 
