Question

Eliminate the parameter t from the following. z(t) = 2 sint - 6 ly(t) = 3 cost - 6 Preview

Answer 1

Eliminate the parameter t from the following set 2 sint - 6 Lyle 3 cost-6 A the given 2(t "Үt) a sint - 6 3 cost – s 2 2 sint - 6 xt6 sint 2 sint - 6+6 [ Adding by sibeth lis And ayt6 = 3 cost - 6+6. 3 cost ztc cost (+6 [Adding by s both side I dividing by both side cost = (1+) - Lise the trigonomatric Formula sin 28 + cos2 = 1 By Equation (1) and in, we get (W+(ii)] sint t + cos2t t) + (116) (246) + (746)=1 (4+6) ? which is 9 Eliminated of parameters of t. (Ans] (at6 + 1

Eliminate the parameter t from the following alt sint - 5 ༽ ༧༤ cost +3 the given parametert from 지 sint - 5 cost + 3 3 [ Adding by 5 e +5 = sint And cost +3 =) y - 3 sint - 5 2+5 = sint -$+$. [ Adding both side) (x+5) sint O Esquaring both side] y (t) cost + 7-8 [ Subtracting by 3 7 (₂-3) = cos cost both side [squaring both side use the formula Equation (U+(1) weget. sinho + Costo = 1 By Equation (isli sinnt + cos²t = (x+ 5)² + (7-3)? + 1 (2+5)2+(4-3) 2=1] [ circle from which is eliminated parametr of t. therefore (ats ²+ +(9939421 Eliminate the parameter & from the following ne(t = 4 + 4 sint ie (Ans) at a cost → the give parametric from at = 4 + 4 sint get) 2+2 cost.

therefore a(t) = 4+4 sint 3) =) x-4 = 4 sin(t) (x-4) A 4 sint sin²t yet [ Subtoactingoy 4 both side [divided by 4 both side] (1) [ both side Squaring sint (2) (2=402 2+2 cast And (1) - 9 use by E =) A y-2 2 cost > Y-2 a cost [both side Cost = (4-2)² =) squaring] the trigonomafric formula binto + cos²8=1 (with a bea angile) quation (I) and (1) we get sin't + cash y (:3)? (x-4) ² (7-2) 2 (21-4) 2 which is 4 eliminated paramenter from. (Parabola) therefore (7.2) 2 Ans) Eliminate the parametest from the following 210 =) + (9-222 16 (x-4)2 16 T = 1 4 5 teint 5 seet N the given parametric from 216 5 tant 5 seet. yet

a = stant tant u by s both side =) tan't [ dividing by * ? [ Squaring both side] (I) And st a 5 seet 2) y sect [ dividing by s both side] (r)" - seent [squaring both side s U) Equation 1 and (1) subtracting we get sect - tan't (3)- 6 ) [poy (0) -(0) 3) 1 2 y 2 x2 25 25 [use formula see20-tam?o=1] therefore y2-22 =25 which is eliminated of parameter from. (Ang) Eliminate the parameter. t from the following the given nst = 6 + 2 tant g(t) at a seet. parametric from nit = 6+2 tant YA at aseet a 6+2 tant X-6 a tant [ subtracting by s beth then T TAIS

x-6 2 tant =) tant =) X-6 A (I ) 7 R-C [ dididing both side by z] tant Squaring both side tant () - And afft y-2= aseet I subtracting by 2 side y-3 [ dividing by 2 both 7-2 sonuaring both side 2+2 seat 1. both - seet seet side seet = (722 T Equation (1) - (I) we get see²t - tan't (1-2) ² (1-2) 2 [use se fromula trigonomatric seeno - tano=1 therefore 1 (4,2) (2-2) 4 - 1 4 (19-22, (2-672 - [ (17-2) - (2-6) = 4 which is eliminating of parameter from 4 (Ans]