...off -fa of the base from each extremity. 4. Solve the equation MR. SALMON. 5. Find the equation of the locus of the foot of the perpendicular from the centre of an ellipse on the line joining the extremities of conjugate diameters. 6. Write down the reciprocals...

...then the equation of the pedal with the point (a, ff)for origin is -e-) = F(xa,y-0) .............. (13). For instance, the locus of the foot of the perpendicular...centre of the ellipse on the common chord (7) is (*2 + y»)» (a?x3 + *V) = (oW- 8V)2 ................ (14). All that has been here said may be applied...

...each other, and touching, respectively, each of three confocal surfaces of the second order. 9. Find the locus of the foot of the perpendicular from the centre of an ellipsoid upon the plane passing through the extremities of a set of conjugate diameters. 10. Find...

...drawn touching the ellipse — a + |j = 1 at Oi 0 any point and passing through the centre; shew that the locus of the foot of the perpendicular from the centre of the ellipse on the chord of intersection of the ellipse and circle is the ... ,. „ ,„ „ 0*6* ellipse a2x + by =...

...that the focus of an ellipse is the pole of the corresponding directrix. 2. Shew that the equation of the locus of the foot of the perpendicular from the centre of an ellipse en a tangent is ri=a"coe,-S v 3. Shew that the Bum of the reciprocals of the squares of...

...(C + ft,) — o. (NEUBERG.) 17. A circle touching an elh'pse passes through its centre : prove that the locus of the foot of the perpendicular from the centre of the ellipse on the chord of intersection is a concentric and homothetic ellipse. 18. All parabolae are similar figures....

...at right angles to it (because it is in the direction of the velocity). Hence the path is such that the locus of the foot of the perpendicular from the centre of acceleration on the tangent is a circle. This property belongs exclusively to conic sections, one focus...

...y sin a =p will touch the same curves if a2 cos2 a ± 62 sin2 a =p2. 28. Show that the equation of the locus of the foot of the perpendicular from the centre of a conic on a tangent is p2 = a2 cos2 в ± ft2 sin2 в. [Use Ex. 27.] 29. If a polar with respect to...

...Find the locus of the foot of the perpendicular from a focus of a central conic to a tangent. 11. Find the locus of the foot of the perpendicular from the centre of an ellipse or hyperbola to a tangent. 12. The slopes of two tangents to an ellipse are connected by...

...that the focus of an ellipse is the pole of the corresponding directrix. 2. Shew that the equation of the locus of the foot of the perpendicular from the centre of an ellipse on a tangent is r2=a2cos20 + fc2sin20. 3. Shew that the sum of the reciprocals of the squares...