...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...

...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...

...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,...

...«"- ' = 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...

...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...

...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 tangent 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...

...o. Put y = zx. .: z+ Integrating, Replacing z by y/x, we have log x = e - -5 - log z. 2. Determine the curve in which the perpendicular from the origin on the tangent is equal to the abscissa of the point of contact. Ans. The circles x* -\- y* = 2cx. 3. Find the curve in which the intercept...

...radius is one-half the vectorial angle (в). [The cardioids r = a (1 — cos 0).] 12. Find the curves in which the perpendicular from the origin on the tangent is equal to the abscissa of the point of contact. [The circles r - 2a cos в.] 13. Find the curves such that the portion of...

...radius is one-half the vectorial angle (ff). [The cardioids r = a (1 — cos 6).] 12. Find the curves in which the perpendicular from the origin on the tangent is equal to the abscissa of the point of contact. [The circles r = 2o cos 6.] 13. Find the curves such that the portion of the...