# 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.)

Read Online or Download Analytical Geometry PDF

Similar geometry & topology books

Lectures on Vector Bundles over Riemann Surfaces. (MN-6)

The outline for this booklet, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), can be coming near near.

Tutor In a Book's Geometry

Need assistance with Geometry? Designed to copy the providers of a talented inner most show, the hot and better teach in a Book's Geometry is at your carrier! TIB's Geometry is an exceptionally thorough, youngster confirmed and powerful geometry educational. TIB’s Geometry comprises greater than 500 of the suitable, well-illustrated, conscientiously labored out and defined proofs and difficulties.

Additional info for Analytical Geometry

Sample text

Obtain the lengths of the tangents from the origin to the circle = 0. x2+y2+7x-4y+16 14. Calculate the length of the tangents from (5, 12) to the circle x2 -f y2=69. 50 ANALYTICAL GEOMETRY 28. Circle with given diameter We now obtain the equation of the circle on the line joining the points A(*i, Ji) and A2(x2, y2) as diameter. Let P(x,y) be a variable point (Fig. 18) on this circle. The gradient of AXP is (y—j>i)/(x—x±) whilst the gradient of A2P is (y-y^Kx-xà· Y Χ' 0 Θ X Υ' FIG. 18 Since ΑλΑ2 is a diameter, the angle AXPA2 is a right angle and so the product of the gradients of the perpendicular lines ΑλΡ and ^ 2 P i s - 1 .

7. Find the coordinates of the circumcentre of the triangle formed by the straight lines 3*-j>-5 = 0, x+2j>-4 = 0 and 5jt+3j> + l = 0. 36 ANALYTICAL GEOMETRY 8. Find the equation of the locus of a point equidistant from (xu y±) and 9. Show that the line joining the points (xl9 yd and (x2, y2) will subtend a right angle at (x3,yz) if (*s—*i) (*s—*2> + (ys—yù (y*—yd = 0. Hence, obtain the equation of the circle on the line joining (xl9 yd and (x2, y2) as diameter. 10. Prove that the straight line (A+2)*+(3A-l)j;+A = 0, where λ is a variable, passes through a fixed point and find its coordinates.

16. Prove that the line-pair x2+4xy+y2 = 0 and the straight line x+y = k form an equilateral triangle. 17. Show that the two line-pairs 1 0 J C 2 + 8 ^ + ^ 2 = 0 and 5x2 + 12xy+6y2 = 0 contain the same angle. 24. Bisectors of the line-pair ax 2 +2hxy+by 2 = 0 Let the line-pair ax2+2hxy+by2 = 0 represent the two dis­ tinct straight lines ^x+m^ = 0 and / 2 x+w 2 j = 0. As in the previous section we have λ/^2 = a ; A(/1/w2+/2Wi) = 2h ; Xm1m2 = b, where λ is some factor of proportionality. The pair of bisectors is given by ΙχΧ+mjy , hx+m^y STRAIGHT LINES 43 That is, (42+^22) (kx+rrny?

Download PDF sample

Rated 4.33 of 5 – based on 49 votes