A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Αποτελέσματα 1 - 5 από τα 37.
Σελίδα 5
... Substitute these values in ( 3 ) and we have PQ2 = r2 + r ̧2 − 2r ̧r , cos ( 0 , — 01 ) . - 12 2 - " This result can also be obtained immediately from the tri- angle POQ formed by drawing lines from P and Q to the origin . 10 . To find ...
... Substitute these values in ( 3 ) and we have PQ2 = r2 + r ̧2 − 2r ̧r , cos ( 0 , — 01 ) . - 12 2 - " This result can also be obtained immediately from the tri- angle POQ formed by drawing lines from P and Q to the origin . 10 . To find ...
Σελίδα 21
... Substitute in the equation , Art . 17 , cos B ' x + = 1 , = 1 , a and we obtain x cos a + y cos B = p . 27. The following form of the equation to a straight line is often useful . B O N M X Let be a fixed point in any line AB ; h , k ...
... Substitute in the equation , Art . 17 , cos B ' x + = 1 , = 1 , a and we obtain x cos a + y cos B = p . 27. The following form of the equation to a straight line is often useful . B O N M X Let be a fixed point in any line AB ; h , k ...
Σελίδα 26
... Substitute in ( 1 ) , thus y = - X1 с -x + c ; - ·· yx , −xy1 + c ( x − x1 ) = 0 . This equation obviously represents a straight line passing through the given point , because it is an equation of the first degree and is satisfied by ...
... Substitute in ( 1 ) , thus y = - X1 с -x + c ; - ·· yx , −xy1 + c ( x − x1 ) = 0 . This equation obviously represents a straight line passing through the given point , because it is an equation of the first degree and is satisfied by ...
Σελίδα 27
... —x1 ) , hence m = x2 - x1 Substitute the value of m in ( 4 ) and we have for the required equation = y - y1 Y2 - yi x - x1 - ( x − x1 ) ( 5 ) . We may also write the equation thus , - ( x , — x ̧ ) ( y — y ̧ ) = ( Y2 — Y1 ) ( x — x ̧ ) ...
... —x1 ) , hence m = x2 - x1 Substitute the value of m in ( 4 ) and we have for the required equation = y - y1 Y2 - yi x - x1 - ( x − x1 ) ( 5 ) . We may also write the equation thus , - ( x , — x ̧ ) ( y — y ̧ ) = ( Y2 — Y1 ) ( x — x ̧ ) ...
Σελίδα 36
... substitute for X1 and Y1 their values in ( 3 ) . Now , since x , y , are the co - ordinates of E , which is the point where ( 1 ) and ( 2 ) meet , we have Y1 = mx1 + c , and Yı - k —— - 1 m - ( x1 − h ) ; - 1 - • , mx1 + c = k − = ( x ...
... substitute for X1 and Y1 their values in ( 3 ) . Now , since x , y , are the co - ordinates of E , which is the point where ( 1 ) and ( 2 ) meet , we have Y1 = mx1 + c , and Yı - k —— - 1 m - ( x1 − h ) ; - 1 - • , mx1 + c = k − = ( x ...
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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.