An Elementary Treatise on Conic Sections |
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Page ix
... Centre - locus of conics touching four fixed lines . [ See also PAGE 137 , 270 , and 297 ] Parabola touching the axes of co - ordinates . Confocal conics Osculating conics Pairs of common chords of two conics . Invariants Examples on ...
... Centre - locus of conics touching four fixed lines . [ See also PAGE 137 , 270 , and 297 ] Parabola touching the axes of co - ordinates . Confocal conics Osculating conics Pairs of common chords of two conics . Invariants Examples on ...
Page 8
... centre is the origin O and whose radius is equal to c , the square of the distance OP will be equal to x2 + y [ Art . 4 ] . But OP is equal to the radius of the circle . Therefore the co - ordinates x , y of any point on the circle ...
... centre is the origin O and whose radius is equal to c , the square of the distance OP will be equal to x2 + y [ Art . 4 ] . But OP is equal to the radius of the circle . Therefore the co - ordinates x , y of any point on the circle ...
Page 10
... centre is at the point ( a , a ) and whose radius is c , is c2 = a2 + r2 − 2ar cos ( 0− a ) ; where r , are the polar co - ordinates of any point on it . - 11. To find the area of a triangle having given the polar co - ordinates of ...
... centre is at the point ( a , a ) and whose radius is c , is c2 = a2 + r2 − 2ar cos ( 0− a ) ; where r , are the polar co - ordinates of any point on it . - 11. To find the area of a triangle having given the polar co - ordinates of ...
Page 42
... centre of any one of the circles are equal in magnitude . The centres of the four circles are therefore [ Art . 31 ] ... centre of the inscribed circle on the sides of the triangle are all drawn in the same direction as those from the ...
... centre of any one of the circles are equal in magnitude . The centres of the four circles are therefore [ Art . 31 ] ... centre of the inscribed circle on the sides of the triangle are all drawn in the same direction as those from the ...
Page 45
... centre of the inscribed circle of the triangle the equations of whose sides are 4y + 3x = 0 , 12y- 5x = 0 , y - 15 = 0 , respectively . 25. Shew that the co - ordinates of the centre of the circle inscribed in the triangle the co ...
... centre of the inscribed circle of the triangle the equations of whose sides are 4y + 3x = 0 , 12y- 5x = 0 , y - 15 = 0 , respectively . 25. Shew that the co - ordinates of the centre of the circle inscribed in the triangle the co ...
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Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre coincident common confocal conics conic touching conjugate diameters constant corresponding Crown 8vo curve diagonals director-circle directrix distance eccentric angles Edition ellipse equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the equation line at infinity line joining line whose equation locus meet middle point nine-point circle normals original conic parabola Pascal's Theorem perpendicular point of intersection points at infinity points of contact polar pole Professor prove quadrilateral radical axis radius ratio rectangular hyperbola right angles second degree self-polar shew sides square tangential equation tangents triangle formed triangle of reference Trinity College values vertex vß² x² y² zero
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