A treatise on plane co-ordinate geometryMacmillan & Company, 1855 |
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Side 68
... external ) and proportional to those sides ; prove that the straight lines . which join the angles with the extremities of the opposite perpendiculars pass through one point . 20. Let the three diagonals of a quadrilateral be produced ...
... external ) and proportional to those sides ; prove that the straight lines . which join the angles with the extremities of the opposite perpendiculars pass through one point . 20. Let the three diagonals of a quadrilateral be produced ...
Side 86
... point passes through the origin of co - ordi- nates , that is , through the centre of the circle . 99. From any external point two tangents can be drawn to a circle . Let the equation to a circle be x2 + y2 = c2 ( 1 ) ... EXTERNAL POINT .
... point passes through the origin of co - ordi- nates , that is , through the centre of the circle . 99. From any external point two tangents can be drawn to a circle . Let the equation to a circle be x2 + y2 = c2 ( 1 ) ... EXTERNAL POINT .
Side 87
... external point - draw the line which is represented by ( 4 ) ; join the points where it meets the circle with the given external point and the lines thus obtained are the required tangents . 101 . Through any fixed point chords are ...
... external point - draw the line which is represented by ( 4 ) ; join the points where it meets the circle with the given external point and the lines thus obtained are the required tangents . 101 . Through any fixed point chords are ...
Side 89
... external point , the equation represents the chord of contact . ( Art . 100. ) III . If ( h , k ) be on the circle , the equation represents the tangent at that point . ( Art . 91. ) In the following figures Q denotes the point ( h , k ) ...
... external point , the equation represents the chord of contact . ( Art . 100. ) III . If ( h , k ) be on the circle , the equation represents the tangent at that point . ( Art . 91. ) In the following figures Q denotes the point ( h , k ) ...
Side 99
... points of inter- section . Also suppose that from any point in ( 3 ) , external to both circles , we draw tangents to ( 1 ) and ( 2 ) ; then , by Art . 108 , these tangents are equal in length . Hence whether ( 1 ) and ( 2 ) intersect ...
... points of inter- section . Also suppose that from any point in ( 3 ) , external to both circles , we draw tangents to ( 1 ) and ( 2 ) ; then , by Art . 108 , these tangents are equal in length . Hence whether ( 1 ) and ( 2 ) intersect ...
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a² sin² a²b² abscissa asymptotes ax² axes axis of x b2 a² b²x² centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant cos² cy² denote directrix distance draw PM ellipse equa equal equation y² external point find the equation find the locus fixed point focal chord focus given point given straight line Hence the equation inclined latus rectum Let the equation line drawn line joining line which passes major axis meets the curve middle point negative ordinate origin of co-ordinates parabola perpendicular point h point of intersection polar co-ordinates polar equation positive preceding article radical axis radius ratio rectangular respectively right angles second degree shew shewn sides Similarly straight line passing suppose tangent tangents are drawn tion triangle vertex x₁ x²² y₁
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