Question

Exercise 3. Find and identify the trace of the given quadric surface in the specified plane of coordinates. f) x2 + 2y – 2z2 – 2 = 0, xz-plane. g) x = y2 + 4, xy-plane. a) A + B + * = 1, xy-plane. b) x2 + 4y2 – 4z2 – 16 = 0, xz-plane. c) -4x2 - y2 + z2 = 1, yz-plane. d) x2 + – z2 = 0, yz-plane. e) x2 + x2 – 4y+4= 0, xy-plane. h) x2 + 4z2 = 4, xz-plane. i) 4z2 – 9y2 = 36, yz-plane.

Answer 1

312) Equation of sy plane is z = 0. x + y + 2 = 1 transforms to 9 254 - 1 which is an ellipse got 25 with major aniso lo CB = 2.a . 2.326.. 7 minor axis - 2.br 2.5=10 (6) Equation of na plane is y ou 0744²-47² - 16 20 transforms to se?-22 = 16 7 2 1 which is a hypertola with major axis - minor axis = 2.4 - 8 (c) Equation of ye plane is a=0. - 42 - y2 + 2 = 1 reduce to - g + 2² - 1, le 22 - y2 = 1 which is a hyperbola with major axis - minor aris. 2. 1 - 2

Equation of yz - Plane is n o u autyzzo reduce to 4 which represents a pair of straight lines passing through the origen. (e) Equation of a y-plane is no & 2² - 44 +420 reduce as x = 44.47 4 (9.1) 1999 toy which represents a parabola with Verten. at A= (0,1) & Equation of na-plano ay =o. x124 - 222 - 2 - 0 reduce as x2 – 27² & 2, se u which 6 a hyp arbola with major ans - 252 and minor anis = 2.1 2. (2)

& Equation of ny-plane is 2-0. x=y+4 7 yr = (2-4) - 4.5 (8-4). parabola with vertex at which ba in ? 2 =1 A È (4,0) (1) Equ. q x2 - plane is y=0. 22 42 4 > > t t 1 which r an ellipse with major anis = 2.2; 4 and minor axis = 2.9 : 2 tqu of yt plave unro A2-'945 336 7 - - SLUTP y2 A UVUVI which is an with major - 3. 2 6 ellipse axis and menor ares = 2.2 =4