 | Dionysius Lardner - Geometry, Algebraic - 1823 - 658 pages
...find the curve in which the perpendicular from the origin on the tangent is constant. (82.) To find the curve in which the perpendicular from the origin on the tangent varies in the subduplicate ratio of the radius vector. (83.) To find the curve in which the locus of... | |
 | Dionysius Lardner - Geometry, Algebraic - 1831 - 582 pages
...find the curve in which the perpendicular from the origin on the tangent is constant. (82.) To find the curve in which the perpendicular from the origin on the tangent varies in the subduplicate ratio of the radius vector. (83.) To find the curve in which the locus of... | |
 | Duncan Farquharson Gregory - Calculus - 1841 - 566 pages
...integral of this is When n = 3, m = 2, this gives the common parabola, as is otherwise obvious. (3) Find the curve in which the perpendicular from the origin on the tangent is equal to the abscissa. The differential equation is dy or «2 — л?8 = 2 a?« — . da> This is a homogeneous equation,... | |
 | D. F. Gregory - Calculus - 1846 - 572 pages
...«"- ' = Cym. When n = 3, го « 2, this gives the common parabola, as is otherwise obvious. (3) Find the curve in which the perpendicular from the origin on the tangent is equal lo ihe abscissa. The differential equation is dy or y" - a? = Zxy -—. ti i This is a homogeneous... | |
 | Bartholomew Price - Calculus - 1854 - 592 pages
...may be equal to the abscissa divided by the ordinate. x ydx—xdy -, ^-- Ex. 3. Find the equation to the curve in which the perpendicular from the origin on the tangent is equal to the abscissa. (xdy-ydx)* = #W, (z*-y*)dx + 2xy dy = O, x^1 y ' x ~~ where 2 a is an arbitrary constant; .-. yz= Zax... | |
 | Bartholomew Price - Calculus - 1865 - 812 pages
...eliminate y', and so obtain the required result. Ex. 3. Prove that the curve in which the length of the perpendicular from the origin on the tangent is equal to the abscissa of the point of contact is the circle, the origin being on the circumference. Ex. 4. Determine the plane curve such that the... | |
 | Samuel H. Winter - 1877 - 452 pages
...to all the lines ? 13. Find the equation to the tangent of the circle y*=2ax — x*, and show that the perpendicular from the origin on the tangent is equal to the abscissa. 14. Prove either analytically or geometrically that the subnormal of a parabola is equal to half the... | |
 | Sir Horace Lamb - Calculus - 1897 - 644 pages
...the radius is one-half the vectorial angle (6). [The cardioids r = a (1 - cos 6).] 9. Find the curves in which the perpendicular from the origin on the...is equal to the abscissa of the point of contact. [The circles r = 2a cos 6.] 10. Find the curves such that the portion of the tangent included between... | |
 | Daniel Alexander Murray - Differential equations - 1898 - 270 pages
...of the curve. ' 16. Find the equation of the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact. 17. Find the equation of a curve such that the projection of its ordinate upon the normal is equal... | |
 | Daniel Alexander Murray - Calculus, Integral - 1898 - 316 pages
...tangent is of constant length a. Ex. 6. Find the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact. Ex. 7. Find the orthogonal trajectories of the straight lines y = ex. Ex. 8. Find the curves orthogonal... | |
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Find the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact. 
