Question

Write the parametric equations x = 2 sin 0, y = 4 cos 0, 0<O< in the given Cartesian form. = with x > 0. 16

Write the parametric equations

x=2siny=4cos0

in the given Cartesian form.

y^2/16= with x0.

Write the parametric equations

x=2sin2y=5cos2

in the given Catesian form.

y= with 0x2.

Write the parametric equations

x=4ety=8e−t

as a function of x in Cartesian form.

y= with x0.

Answer 1

Solution:- Cuirer parametoic equation = 2 Sino -(1) , y = 4 cos o OC OKT x2=(sing? => x² = 4 sinzo Therefore / sin 20 = 22 Similarly (9)2 = (400sol > y² = 16 cos20 > 42 16 coslo since coslot sino = 1 >cos2o=d-Sinzo y² 16 02415T = -> 42 T = 16 Since 4 en from equataonli) Therefore yZ 16 4-x² 4 cortesian form walth ago Answer

Soledion- Giiren parametric equation A24750 Eve () 2250 SER (C >18 caso From equation ) Sin20 2 since Cashots020=1 » sono=1-c0520 2 = 1 - costo → X 2 Si- 1- 5 since cos?o= 4 5 aloc XT 2 > y = 2.- => y = 5(2-x) 2 Therefore y = 104-57 2 Answer ; 03*32

Solado: Given parametric equation x=4et •Y=set (ii) From equation a 7 3 = et Taking logarithon both side we get enlar) let) lo (24) = + inte) since enleja --> 110 ln (*)=t رأن from equestion Li) weget y = set > y = 8 et => gi et = 8 => et 8 y Taking logarithm both sidcloeget enlet), enlig

since enxo =alex) => t dole) = lolog - t.l=en 1(044 smce In (e)=1 taly & 13) LV) Put the value of it) obtained in equation (iv) in portion (ji) weget Swiss) We know that en(a)=ln (9) Im (b) ng ln(x) -enl4) -- en 18) -enly). > lnly) - enten (4) -en (3) -> enly)= eri( 3443) - lag en (9) flo(b) =lo (ab) -- 19- 32)-(2) - en (Y) = en 10321 Therefore G= 32 re with x70 Answer