...hence by substitution 2/7 2a TO 2 TO y=mx+— ; m •which is the equation to the tangent in terms of the tangent of the angle which the line makes with the axis of the parabola. 80. To find the equation to the normal at any point on a parabola. Let (x', 2/') be the...

...radius =2a=DS. 9. Let 7/2=4aa; be the equation to the parabola. The equation to the tangent, in terms of the tangent of the angle which the line makes with the axis, is y'=mx' + — , or m2— ¥-, m+ — , =0 : m o> of solving this quadratic, we obtain bat a;'= ^-—...

...—, maybe written y = —- x 4- —, or, if —7 be denoted by m, V y 2a' y 1 J ym — — (1} Here m is the tangent of the angle which the line makes with the axis of x. Conversely any line whose equation is of the form y — x tan 0 + a cot #, touches the parabola y*...

...y' -e 2a . , . , , y= — x+ ^~ , or, it —7 be denoted by m, y 2a y y = mx-\ — ••(!)• Here m is the tangent of the angle which the line makes with the axis of x. Conversely any line whose equation is of the form y = x tan 6 + a cot 0, touches the parabola y' =...

...conveniently written y — II' X — X' 7 . where s and c are abbreviations for the sine and cosine of the angle which the line makes with the axis of x. 1O2. Geometric meaning of the ratio /.—If, in the annexed diagram, P' denote the fixed point x'y',...

...after reduction, y = ax -\- b, which is the common equation of the straight line. In this equation a is the tangent of the angle which the line makes with the axis of abscissas, and b the distance from the origin to where the line intersects the axis of ordinates. SCH....

...coefficient — '-— as obtained in the several x — x c«ses in Ex. 4, 10, and 1. But this coefficient is the tangent of the angle which the line makes with the axis of x (31, COB. 1). , Ex. 1. What angle does a tangent to ya = Bx make with the axis of x, when the point...

...co-efficient we have divided the equation. Illustration. If 3y=6x— 9, then y — 2x— 3. Here 2 is the tangent of the angle which the line makes with the axis of a;, and —3 is the distance from the origin to the point where the line cuts the axis of y. Or, solving...

...expression for the length of the portion of the line which is intercepted between the two curves in terms of the angle which the line makes with the axis of x. 24. Prove that in order to find the differential co-efficient of a defi::::e integral with respect...

...ratio to each, other. Also, it is evident that m = -'-, which in rectangular 33 . axes = tan XOP, ie = tangent of the angle which the line makes with the axis of x. When a line does not pass through the origin, its equation can be found thus :—Draw through the origin...