David Eugene Smith

Analytic Geometry David Eugene Smith Large Type edition

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 Excerpt: ...being (--3, 4). 6. y2 = 12 a;, through the point (--2,--5). The given point is not on the parabola. Let y = mx + 3/ro be the tangent, and find m from the condition that (--2,--5) is on the tangent. 7. x = 2 y2, from the point (8,--2). 8. 2tf + Ix = 0, from the point (-3, Y) 9. Sy2 =--ix, having equal intercepts. 10. Show that the line y=--Sx + 2 is tangent to the parabola y2 =--24 x, and find the point of contact. 11. Find the point of contact of the line which is tangent to the parabola y2 = 3 x and has the slope 12. Find in terms of m the coordinates of the point of contact of the tangent with slope m to the parabola y2 = ipx. 13. Show that the intercepts of the tangent with slope m to the parabola y2 = ipx are--p/m2 &n6.p/m. 14. A line with slope m is tangent to the parabola 5 y2 = 8 x and forms with the axes a triangle of area 10. Find m. 15. A line with slope m is tangent to the parabola 3 y2--80 x and is also tangent to the circle x2 + y2 = 9. Find m. 16. If the line x--2y + 12 = 0 is tangent to the parabola y2 = cx, find c. 17. If two tangents to a parabola are perpendicular to each other, they meet on the directrix. PATH OF A PKOJECTILE 131 Problem. Path Of A Projectile 132. To find the path of a projectile when the initial velocity is given, disregarding the resistance of the air. Solution. Take as axes the horizontal and vertical lines through the initial position of the projectile. Let the initial velocity be v, directed at the angle a with OX. Without the action of gravity the projectile would continue in the straight line OQ, and after t seconds would reach a point Q distant vt from O; that is, OQ--vt. But the action of gravity deflects the projectile from OQ by a vertical distance PQ, which in t seconds is I gt2. It is assumed that the stu...