An Elementary Treatise on Conic Sections |
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... fixed points 295 Conics touching four fixed lines 296 Conics with respect to ... point circle 299 Pascal's theorem . [ See also 328. ] 299 Brianchon's ... point 320 Co - axial circles reciprocated into confocal conics 322 Projection ...
... fixed points 295 Conics touching four fixed lines 296 Conics with respect to ... point circle 299 Pascal's theorem . [ See also 328. ] 299 Brianchon's ... point 320 Co - axial circles reciprocated into confocal conics 322 Projection ...
Page 9
... fixed points ( a , 0 ) and ( −a , 0 ) is constant ( 2c2 ) ; find the equation of its locus . Ans . x2 + y2 = c2 — a2 . Ex . 3. A point moves so that the difference of the squares of its distances from the two fixed points ( a , 0 ) and ...
... fixed points ( a , 0 ) and ( −a , 0 ) is constant ( 2c2 ) ; find the equation of its locus . Ans . x2 + y2 = c2 — a2 . Ex . 3. A point moves so that the difference of the squares of its distances from the two fixed points ( a , 0 ) and ...
Page 40
... point . [ Art . 34. ] ( 2 ) Any straight line is drawn through a fixed point A cutting two given straight lines OX , OY in the points P , Q respectively , and the paral- lelogram OPRQ is completed : find the equation of the locus of R ...
... point . [ Art . 34. ] ( 2 ) Any straight line is drawn through a fixed point A cutting two given straight lines OX , OY in the points P , Q respectively , and the paral- lelogram OPRQ is completed : find the equation of the locus of R ...
Page 41
... point R always satisfy the relation ( ii ) . Calling the co - ordinates of the point R , x and y instead of a and ẞ , we have for the equation of its locus + 2 = 1 . x y ( 3 ) Through a fixed point O any straight line is drawn meeting ...
... point R always satisfy the relation ( ii ) . Calling the co - ordinates of the point R , x and y instead of a and ẞ , we have for the equation of its locus + 2 = 1 . x y ( 3 ) Through a fixed point O any straight line is drawn meeting ...
Page 43
... fixed point . 2. Prove that bx3 - 2hxy + ay = 0 represents two straight lines at right angles respectively to the ... fixed straight lines , A , B being fixed points ; P , Q are any two points on these lines such that the ratio of AP to ...
... fixed point . 2. Prove that bx3 - 2hxy + ay = 0 represents two straight lines at right angles respectively to the ... fixed straight lines , A , B being fixed points ; P , Q are any two points on these lines such that the ratio of AP to ...
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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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