 | Dublin city, univ - 1866 - 300 σελίδες
...regard to an equilateral hyperbola passes through the cenlre of the curve ? 3. In the curve x" + ya = a", find the length of the perpendicular from the origin on the tangent, and of the intercept made on the tangent between the axes. 4. Find an expression for the length of... | |
 | Benjamin Williamson - 1872 - 372 σελίδες
...the subnormal in the parabola, y* =px, is equal to -. 156. Perpendicular on the Tangent. — Let/1 be the length of the perpendicular from the origin on the tangent at any point on the curve F(x, y) = c, then the equation of the tangent may be written + Ysinш=p, where... | |
 | Isaac Todhunter - 1873 - 452 σελίδες
...y) = a* (x—y), the equation to the tangent at the origin is у = x. 5. In the curve a$ + yb = cfi find the length of the perpendicular from the origin...tangent which is intercepted between the two axes. Eesults. (1) i/(axy) ; (2) a. 6. If xi" уг, be the parts of the axes of x and у intercepted by the... | |
 | Benjamin Williamson - 1873 - 394 σελίδες
...whose equation is xyt = a1 (a — x), is a minimum. 1 68. Perpendicular on the Tangent. — Let p be the length of the perpendicular from the origin on the tangent at any point on the curve F(x, y) = c, then the equation of the tangent may be written X cos ш + T ein... | |
 | Isaac Todhunter - 1875 - 440 σελίδες
...curve x" (x + y) = a' (x—y), the equation to the tangent at the origin is y = x. 5. In the curve o$ + y' = a* find the length of the perpendicular from...tangent which is intercepted between the two axes. Eesults. (1) \l(ctxy); (2) a. 6. If or,, yt, be the parts of the axes of a; and y intercepted by the... | |
 | Isaac Todhunter - 1881 - 440 σελίδες
...x* (x + y) = a 2 (x—y), the equation to the tangent at the origin is y = x. 5. In the curve o$ + y^ = a* find the length of the perpendicular from the origin on the tangent at (a;, y) ; also find the length of that part of the tangent which is intercepted between the two axes.... | |
 | Woolwich roy. military acad - 1884 - 148 σελίδες
...Prove that the equation of the tangent at the point (x, y) of the curve u=f(x, y) = o is . . du du Find the length of the perpendicular from the origin on the tangent at the point (x, y) of the curve 6. Define a point of inflexion, and state the analytical condition for... | |
 | Joseph Edwards - 1886 - 540 σελίδες
...following curves : — (a) (a;2 + 7/2)2 = a2a:2_6-y->. 08) fr-«)<^£-* (y) a;3 + y5 = 5ax2i/2. 3. Find the length of the perpendicular from the origin on the tangent at the point x, y of the curve 4. Show that in the curve y = be "the sub tangent is of constant length.... | |
 | E. J. Brooksmith - 1889 - 356 σελίδες
...APYis \*Ji 5. Prove that the equation of the tangent at the point (x, y) of the curve u=f(x, y)=o is Find the length of the perpendicular from the origin on the tangent at the point (x, y) of the curve 6. Define a point of inflexion, and state the analytical condition for... | |
 | Joseph Edwards - 1892 - 550 σελίδες
...axis of x we have as in Art. 37, , , , and also cos \L = . , ,. and sin \ls = Lt -.— EXAMPLES. 1. Find the length of the perpendicular from the origin on the tangent at the point x, y of the curve xt+yt = c4. X 2. Show that in the curve y = b(f the subtangent is of constant... | |
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In the curve x*y* = a* (x + y], the tangent at the origin is inclined at an angle of 135° to the axis of a:. 4. In the curve x" (x + y) = a' (x—y), the equation to the tangent at the origin is y = x. 
