An Elementary Treatise on Conic Sections |
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Page 5
... shew that the distance between them is 5 . Ex . 2. Find the lengths of the lines joining the following pairs of ... Shew that the three points ( 1 , 1 ) , ( − 1 , − 1 ) and ( −√3 , √3 ) , are the angular points of an equilateral ...
... shew that the distance between them is 5 . Ex . 2. Find the lengths of the lines joining the following pairs of ... Shew that the three points ( 1 , 1 ) , ( − 1 , − 1 ) and ( −√3 , √3 ) , are the angular points of an equilateral ...
Page 14
... shew that every equation of the first degree represents a straight line . The most general form of the equation of the first degree is Ax + By + C = 0 ........ .. ( i ) To prove that this equation represents a straight line , it is ...
... shew that every equation of the first degree represents a straight line . The most general form of the equation of the first degree is Ax + By + C = 0 ........ .. ( i ) To prove that this equation represents a straight line , it is ...
Page 23
... Shew that the three lines 5x + 3y - 7 = 0 , 3x - 4y - 10 = 0 , and x + 2y = 0 meet in a point . - 10. Shew that the three points ( 0 , 11 ) , ( 2 , 3 ) and ( 3 , 1 ) are on a straight line . Also the three points ( 3a , 0 ) , ( 0 , 3b ) ...
... Shew that the three lines 5x + 3y - 7 = 0 , 3x - 4y - 10 = 0 , and x + 2y = 0 meet in a point . - 10. Shew that the three points ( 0 , 11 ) , ( 2 , 3 ) and ( 3 , 1 ) are on a straight line . Also the three points ( 3a , 0 ) , ( 0 , 3b ) ...
Page 24
Charles Smith. А 17. Shew that the points ( 0 , 0 ) and ( 3 , 4 ) are on opposite sides of the line y -2x + 1 = 0 . 18. Shew that the origin is within the triangle the equations of whose sides are x - 7y + 25 = 0 , 5x + 3y + 11 = 0 , and ...
Charles Smith. А 17. Shew that the points ( 0 , 0 ) and ( 3 , 4 ) are on opposite sides of the line y -2x + 1 = 0 . 18. Shew that the origin is within the triangle the equations of whose sides are x - 7y + 25 = 0 , 5x + 3y + 11 = 0 , and ...
Page 30
... shew that the equation of the line joining these points is 23x + 11y - 35 = 0 . 4. Find the perpendicular distances of the point ( 2 , 3 ) from the lines 4x + 3y - 7 = 0 , 5x + 12y - 20 = 0 , and 3x + 4y - 8 = 0 . Ans . 2 . - 5. Write ...
... shew that the equation of the line joining these points is 23x + 11y - 35 = 0 . 4. Find the perpendicular distances of the point ( 2 , 3 ) from the lines 4x + 3y - 7 = 0 , 5x + 12y - 20 = 0 , and 3x + 4y - 8 = 0 . Ans . 2 . - 5. Write ...
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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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