Analytical Geometry by Barry Spain, W. J. Langford, E. A. Maxwell and I. N. Sneddon

By Barry Spain, W. J. Langford, E. A. Maxwell and I. N. Sneddon (Auth.)

Show description

Read Online or Download Analytical Geometry PDF

Similar geometry & topology books

Notions of Convexity

The 1st chapters of this booklet are dedicated to convexity within the classical feel, for capabilities of 1 and a number of other genuine variables respectively. this offers a historical past for the research within the following chapters of comparable notions which happen within the thought of linear partial differential equations and complicated research akin to (pluri-)subharmonic capabilities, pseudoconvex units, and units that are convex for helps or singular helps with recognize to a differential operator.

Plane and Solid Analytic Geometry

The item of an ordinary collage direction in Analytic Geometry is twofold: it's to acquaint the coed with new and engaging and significant geometrical fabric, and to supply him with strong instruments for the learn, not just of geometry and natural arithmetic, yet in no much less degree of physics within the broadest experience of the time period, together with engineering.

Additional resources for Analytical Geometry

Sample text

Obtain the equations of the circles which touch the *-axis at (5, 0) and make an intercept of 24 on the >>-axis. 32. Condition that a line be tangent to a circle Tf the straight line lx+my+n = 0 is a tangent to the circle x2+y*+2gx+2fy+c = 0 the perpendicular from the centre (—g, —f) to the line lx+my+n = 0 is equal to the radius \/{g2+f2—c). +ft ) and so (-Ig-mf+nf = (/ 2 +m 2 ) ( g 2 + / 2 - c ) which reduces to (c-f2)l2+2fglm+(c-g2)m2-2fmn-2gnl+n2 = 0. This formula is too cumbersome to be remembered.

X2—y2) — 2(lxm2—i2m^) (l1l2—fn1m2)xy = 0. Since the lines of the line-pair are distinct, l1m2—l2m1 Φ 0 and so division by lxm2-l2m1 yields {iim2+l2m^) (x2—y2) — 2(l1I2—m1m2)xy = 0. Substituting for lj2, m1m2 and Ιχηί2-{-12ηι^ we have h(x2-y2) - (a-b)xy = 0. EXAMPLES 18. Write down the equation of the line-pair bisecting the angles between the line-pairs (i) x2—y2 = 0; (ii) 4x2—xy—3y2 = 0; (iii) x2 cos Ö+2^-^ 2 sin Θ = 0. 19. Show that x—y = 0 bisects the angle between the lines Ax2— \\xy+4y2 = 0 and write down the equation of the other bisector.

Cf and so αχχ+by^+c d=± The sign of d is indeterminate, but from the previous section we see that the lengths of the perpendiculars from points on the same side of the straight line have the same sign. FIG. 14 If the equation is written in the normal form x cos α+j; sin a=p, the perpendicular distance from (xl9 νλ) is ± (*i COS a + J i Sin a—p). EXAMPLES 49. Calculate the perpendicular distances from (2, —1) to the straight lines; (i) 4x+3y = 2; (ii) * - ^ + 1 = 0; (iii) 2x-3y-l = 0. STRAIGHT LINE 29 50.

Download PDF sample

Rated 4.02 of 5 – based on 20 votes