A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Σελίδα 99
... and the circle х 22 + 3/2 - 1 1 = 0 , y k x2 + y2 — 2ax — 2by = 0 . - - Deduce the relation that must hold in order that the line may touch the circle . 9. Find the equation to the tangent at the origin 7-2 EXAMPLES ON THE CIRCLE . 99.
... and the circle х 22 + 3/2 - 1 1 = 0 , y k x2 + y2 — 2ax — 2by = 0 . - - Deduce the relation that must hold in order that the line may touch the circle . 9. Find the equation to the tangent at the origin 7-2 EXAMPLES ON THE CIRCLE . 99.
Σελίδα 101
... touch each other . 23. ABC is an equilateral triangle ; take A as origin , and AB as axis of x ; find the ... touching the circle at a given point . 25. Find the polar equation to the circle , the origin being on the circumference and ...
... touch each other . 23. ABC is an equilateral triangle ; take A as origin , and AB as axis of x ; find the ... touching the circle at a given point . 25. Find the polar equation to the circle , the origin being on the circumference and ...
Σελίδα 105
... touch both circles , the lengths of these lines are equal . 110. An equation of the form A ( x2 + y2 ) + Bx + Cy + D = 0 will represent a circle ; for after division by A we obtain the ordinary form of the equation to a circle . We ...
... touch both circles , the lengths of these lines are equal . 110. An equation of the form A ( x2 + y2 ) + Bx + Cy + D = 0 will represent a circle ; for after division by A we obtain the ordinary form of the equation to a circle . We ...
Σελίδα 106
... to the line joining the centres of the circles is ( Art . 35 ) - y - b = b b ( x − a ) α - α - ( 1 ) and ( 2 ) are at right angles by Art . 42 . .... ( 2 ) ; 114. When two circles touch , their radical axis is 106 RADICAL AXIS .
... to the line joining the centres of the circles is ( Art . 35 ) - y - b = b b ( x − a ) α - α - ( 1 ) and ( 2 ) are at right angles by Art . 42 . .... ( 2 ) ; 114. When two circles touch , their radical axis is 106 RADICAL AXIS .
Σελίδα 107
... touch two given circles . If the circles do not intersect , four common tangents can be drawn ; two of them will be equally inclined to the line joining the centres , and will intersect on that line between the circles ; the other two ...
... touch two given circles . If the circles do not intersect , four common tangents can be drawn ; two of them will be equally inclined to the line joining the centres , and will intersect on that line between the circles ; the other two ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b²x² bisects centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant Crown 8vo cy² denote directrix distance Edition ellipse equa equal Examples external point find the equation find the locus fixed point focal chord focus given lines given point Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly student suppose tangent tion triangle vertex x₁ y₁
Δημοφιλή αποσπάσματα
Σελίδα 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 304 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Σελίδα 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Σελίδα 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Σελίδα 189 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.