 | W. J. Johnston - Geometry, Analytic - 1893 - 448 pages
...tangent at any point meets the directrix and latns rectum at points equidistant from the focus. 9. Find the locus of the foot of the perpendicular from the focus on the normal. Ans. The parabola y2 = a (x — a). 10. Prove that the parabolas y2 = ax, x2 = by ¡a cut at an angle... | |
 | History - 1893 - 304 pages
...joining the fourth point of these two ranges is a conic touching the double and inflectional tangents. The locus of the foot of the perpendicular from the focus on the tangent to a conic is the auxiliary circle. Inverting: — draw a circle through the node tangent to... | |
 | History - 1893 - 294 pages
...joining the fourth point of these two ranges is a conic touching the double and inflectional tangents. The locus of the foot of the perpendicular from the focus on the tangent to a conic is the auxiliary circle. Inverting: — draw a circle through the node tangent to... | |
 | 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... | |
 | Sidney Luxton Loney - Coordinates - 1896 - 447 pages
...A parabola circumscribes a right-angled triangle. • Taking its sides as the axes of coordinates, prove that the locus of the foot of the perpendicular from the right angle upon the directrix is the curve whose equation is 2xy (x2 + y2) (hy + kx) + h2ij* + 7cV=... | |
 | 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... | |
 | 1898 - 872 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 from the... | |
 | 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... | |
 | Clement Vavasor Durell - Geometry, Plane - 1910 - 392 pages
...then PAQ is constant. 144. Reciprocate wrt 0 : AB is a diameter of a circle AOPB ; then APB=qo°. 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... | |
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The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the major axis as diameter. 3. The locus of the point of intersection of perpendicular tangents is a circle with radius Va> 
