An Elementary Treatise On Analytical Geometry, With Numerous Examples
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= constant, the locus of P is a circle whose centre is the mean centre of the points A, B, C, &c. for the system of multiples m lt m 2 , &c.
i 5 8 Analytical Geometry 1 1 . A point moves so that the sum of the squares of its distances from the sides of a regular polygon is constant : show that its locus is a circle.
[Equation to locus is (x cos a + y sin OL — p) 2 ( a + V>ysin( a+ V>p] 2 Then x cos = constant coefP of xy = sin 2 a + sin ( 2 OC + —J + sin ( 2 OC + — 1 + ... = o * Also coeff' of ...x 2 — coefF of y 2 = COS 2 £X + COS I 2 OC + ?— 1 + COS ( 2 & + 1 + ...= OJ 12. On a line which revolves round a fixed point O and meets a given circle in P a point Q is taken such that OP.OQ = constant = k 2 ; show that the locus of Q is a circle except in the case when O is on the given circle, when the locus is a straight line.
[Proceed as in § in, Ex. i. The locus of Q is the inverse (see Euclid Revised, p. 351) of the given circle. Accordingly the inverse of a circle is a circle, unless the centre of inversion is on the given circle, when the inverse is a straight line.] 13.
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To quickly assess the difficulty of the text, read a short excerpt:
= constant, the locus of P is a circle whose centre is the mean centre of the points A, B, C, &c. for the system of multiples m lt m 2 , &c.
i 5 8 Analytical Geometry 1 1 . A point moves so that the sum of the squares of its distances from the sides of a regular polygon is constant : show that its locus is a circle.
[Equation to locus is (x cos a + y sin OL — p) 2 ( a + V>ysin( a+ V>p] 2 Then x cos = constant coefP of xy = sin 2 a + sin ( 2 OC + —J + sin ( 2 OC + — 1 + ... = o * Also coeff' of ...x 2 — coefF of y 2 = COS 2 £X + COS I 2 OC + ?— 1 + COS ( 2 & + 1 + ...= OJ 12. On a line which revolves round a fixed point O and meets a given circle in P a point Q is taken such that OP.OQ = constant = k 2 ; show that the locus of Q is a circle except in the case when O is on the given circle, when the locus is a straight line.
[Proceed as in § in, Ex. i. The locus of Q is the inverse (see Euclid Revised, p. 351) of the given circle. Accordingly the inverse of a circle is a circle, unless the centre of inversion is on the given circle, when the inverse is a straight line.] 13.
What to read after An Elementary Treatise On Analytical Geometry, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Johnston, W. J., D. 1924 to read onlineMoreLess
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