...vertex is an ellipse. 50. Show that the equation to the normal of an ellipse expressed in terms of the tangent of the angle which the line makes with the axis of x is у = mx — m 57. In the ellipse x* + 4yf = 9, show that the locus of the middle points of all chords...

...because it is evidently satisfied when x' and y' are substituted in it for x and y. The constant a is the tangent of the angle which the line makes with the axis of x, or the ratio of the sines of the angles which the line makes with the two axes respective! y, according...

...the straight line, a and b denote the intercepts of the line on the axes of x and y respectively, TO the tangent of the angle which the line makes with the axis of x, p the perpendicular on the line from the origin, a the angle which this perpendicular makes with the...

...observations, and hence a and h are the quantities tobo derived from the equations. The quantity a becomes 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 ordiuates. In...

...assume the form a cos a + b sin a — p = ± r. (2) 69. Equation of the tangent expressed in terms of the tangent of the angle which the line makes with the axis of X. Let y = mx -j- b be the equation of the tangent, and x' + y' = r' the equation of the circle. Eliminating...

...— , or ^-=— ; henco by substitution 2a m 2 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 (x1, y') be the...

...showing •he relation between them is practically a right line, whoso equation is v'=an+b, ¡n which a is the tangent of the angle which the line makes with the axis of abscisfa *- aud b tho distance from the origin to tho point of intersection with the axis of "Hliuatcs....

...equation of any straight line through this point may be expressed in the form yy t =m(x- a;,); (5) m being the tangent of the angle which the line makes with the axis of X. But we have shown (§ 20) that m = -p, dx, dy, this differential coefficient being formed by differentiating...

...If the independent term (7=0, through what point does the line pass? In the equation Ax+By=0, what is the tangent of the angle which the line makes with the axis of X? Upon which of the parameters does the direction of line (/) depend? 2. If A = 0, By + C= 0 ; if B =...

...commonly used for it is - , where c is the capacity for y, V \p, M* V," w. \ •• V. tf4 gradient), is the tangent of the angle which the line makes with the vertical within the several strata. Accordingly it appears that, if observations are taken at underground...