 | Pierce Morton - Geometry - 1830 - 584 pages
...= x - -— = x tan. ( 45° + - — ) and cos. a \ 2 / therefore the lines pass through the origin, and are inclined to the axis of x at angles of 45° ± — . 327. Since the general equation includes all equations below it, the properties of the curve... | |
 | Mathematics - 1835 - 684 pages
...= x - = x tan. I 45° + • — I and cos. a \ — 2 / therefore the lines pass through the origin, and are inclined to the axis of x at angles of 45° ± -^-. 327. Since the general equation includes all equations below it, the properties of the curve... | |
 | William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...coincides with a parabola of which y — ax is the equation of a diameter. II. If r = 2, /»£<--*(«); is the equation of two straight lines which are asymptotes to the curve. To trace the curve whose equation is xy(y-xf - ay3 = a4. When x = 0, y = — a, x cannot be negative... | |
 | Cambridge univ, exam. papers - 1854 - 284 pages
...ultimately coincides with a parabola of which y = ax is the equation of a diameter. II. If r = 2. - 20 (a) is the equation of two straight lines which are asymptotes to the curve. To trace the curve whose equation is xy(y-xf - ay3 = a\ When x = 0, y = — a, x cannot be negative... | |
 | Edward Henry Courtenay - Calculus - 1855 - 526 pages
...o X i £ ing powers of 2). Hence y =±(.r — -i) is the equation of two straight lines, which arc asymptotes to the curve, and are inclined to the axis...on the right of the axis of y. Forming the value of — from the equation of the curve, we have CIX dy 2x3 + 3bxz + a3 fir 18 2 (*=» - «3r (* + rf which,... | |
 | Edward Henry Courtenay - Calculus - 1857 - 522 pages
...given equation with respect to y, and expanding, we get t = ±*fl — jy-+ £-5, &c.l= ± (* — o& + terms involving powers of x). Hence y = ±(x — -6)...the right of the axis of y. .Forming the value of -2- from the equation of the curve, we have dy 2J2 + 3fo2 + a2 ' 2(x2 - a (x + b)« which, placed equal... | |
 | Edward Henry Courtenay - Calculus - 1860 - 516 pages
...4PowersofⅠ じ Ⅰ 面 C ・二） Hence y @ (#b) is the equation of two straight lines, which & are asymptotes to the curve, and are inclined to the axis of x at angles of 45 and 135 respectively. Jf we combine this equation of these asymptotes with that of the curve, we shall find that each of... | |
 | Edward Henry Courtenay - Calculus - 1873 - 524 pages
...о x / ii ing powers of x). Hence у = ±(x — -b) is the equation of two straight lines, which m are asymptotes to the curve, and are inclined to the...on the right of the axis of y. Forming the value of -f- from the equation of the curve, we have ax dy 2*3 + 3fti2 + a? - a3) (x + ¿) which, placed equal... | |
 | Edward Henry Courtenay - Calculus - 1873 - 528 pages
...i)1 = ±x(l---4-g— , &C.J = d= (x — - b + terms involving powers of x). Hence у = ±(x — -b) is the equation of two straight lines, which are asymptotes...axis of x at angles of 45° and 135° respectively. Jf we combine this equation of these asymptotes with that of the curve, we shall find that each of... | |
 | Thomas Kimber - 1880 - 176 pages
...instructions given in Art. 290. In 2nd equation, x = + y, giving two lines intersecting in the origin, and inclined to the axis of x at angles of 45° and 135° respectively. 14. (1) Art. 314. (2) From the question, i/2 = 4ae; с •=• у — bx, we have by multiplying the... | |
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Hence y — ±(x — - 6) is the equation of two straight lines, which are asymptotes to the curve, and are inclined to the axis of x at angles of 45° and 135° respectively. If we combine this equation of these asymptotes with that of the curve, we... 
