...= o2 — 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...

...= o2 — 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...

...if is a diameter, and the segment TM is bisected by its point of intersection with the curve. 7 4. The locus of the foot of the perpendicular from the focus on a moving tangent is the tangent at the vertex. 5. The locus of the point of intersection of perpendicular...

...remember: 1. The normal at any point P bisects the angle formed by the lines joining P with the foci. 2. 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...

...remember: 1. The normal at any point P bisects the angle formed by the lines joining P with the foci. 2. 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...

...remember: 1. The normal at any point P bisects the angle formed by the lines joining P with the foci. 2. 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...

...The tanFio. 51. FIG. 52. Fia. 53. loot at any point P (Fig. 51) bisects the angle between PF and PF'. The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the principal axis as diameter (Fig. 52). The locus of the point...

...The tanFia. 51. FIG. 52. FIG. 53. gent at any point.? (Fig. 51) bisects the angle betweenPf andPi". The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the principal axis as diameter (Fig. 52). The locus of the point...

...tanFiu. 51. Fiu. 52. F1u. 53. gent at any point P (Fig. 51) bisects the angle between Pi' and Pi". The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the principal axis as diameter (Fig. 52). The locus of the point...

...now inquire what is the pedal of an n-fold parabola with regard to the focus, that is to say, what is the locus of the foot of the perpendicular from the focus on the tangent. It is easy to prove — as was pointed out by Dr Hirst — that this pedal is the inverse...