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TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES MANILA ANALYTIC ANALYTIC GEOMETRY NAME:__________________________________ DATE:JULY 30, 2014 ENGR. LORRAINE CARRILLO INSTRUCTIONS: Enc!c"# $%# c&!!#c$ 'n()#! 'n* +!&*# $%# (&"-$&n( &! +!&/"# (&"n -#($&n( 1. Give iven an el ellips lipsee (x (x2 / 36) + (y 2 / 32) = 1. Determine the distance between the !ci. a. " b. # c. 2 d. 3
2.
3.
#.
.
$he se%m se%ment ent r!m r!m (&1'#) (&1'#) t! (2'&2 (2'&2)) is extende extended d three three times times three times its !wn len%th. $he terminal p!int is a. (11'&2#) b. (&11'2) c. (11'&1") d. (11'&2) 2
2
ind ind the the val*e val*e ! !r which which the the e,*at e,*ati!n i!n x + y + #x - 2y - = represents a p!int circle. a. b. 6 c. & d. &6
!int !int (x'y (x'y)) m!ves m!ves with with a distanc distancee r!m p!in p!intt ('1) ('1) !ne hal ! its distance r!m line y = #. $he e,*ati!n ! its l!c*s is a. 2x2&#y2= b. #x2+3y2= 2 2 c. 2x +y =3 d. x2+2y2=# ind ind the area area ! the tria trian% n%le le which which the line line 2x&3y 2x&3y+6 +6= = !rm with the c!!rdinate axes. a. 3 b. # c. d. 2
6.
0 the p!int p!intss (&2'3)' (&2'3)' (x'y (x'y)) and (&3') (&3') lip lip !n a strai%ht strai%ht line' line' then the e,*ati!n ! the line is a. x&2y&1= b. 2x+y&1= c. x+2y&1= d. 2x+y+1=.
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ind ind the c!!rd c!!rdina inates tes ! the the vertex vertex ! the the parab! parab!la la y=x2& #x+1 by main% *se ! the act that at the vertex' the sl!pe ! the tan%ent line is er!. a. (2'&3) b. (&2'&3) c. (&1'3) d. (3'&2)
".
.
$he parab!lic antenna has an e,*ati!n Determine the len%th ! the lat*s rect*m. a. " b. 1 c. 12
y2+"x=.
c. "2.#
d. 2.#
13. ind ind the val*e ! i the distance distance r!m r!m the p!int (2'1) (2'1) t! the line x+12y+= is 2. a. b. 2 c. # d. 3 1#. Determin Determinee the arthest arthest distance distance r!m r!m the p!int (3') (3') t! the 2 2 circle x +y +#x&6y&12=. a. 6.# b. 1.# c. 11.# d. #.6
1. 0 the lines lines #x&y+2= #x&y+2= and x+2y+1= x+2y+1= are perpendic perpendic*lar *lar t! each !ther' determine the val*e ! . a. 3 b. # c. 1 d. 2
16. 9hat 9hat is the e,*ati e,*ati!n !n ! the line line thr!*% thr!*%h h (&3' (&3')) which which maes an an%le ! # de%rees with the line 2x+y=12: a. x+3y&12= b. x+3y+1"= c. x+2y&= d. x&3y&1"= 1. Determin Determinee the e,*ati!n e,*ati!n ! the perpendic*la perpendic*larr bisect!r bisect!r ! the se%ment ; i (&2'3) and ;(#'&). a. 3y&3x+= b. #x&3y+= c. 6x&"y&1#= d. 3x&#y&= 1". 0 the p!ints p!ints (&3'&)' (&3'&)' (p',) (p',) and (3'#) (3'#) lie !n a strai%ht strai%ht line' line' which ! the !ll!win% is c!rrect: a. 2p&3,=1 b. p+,=&3 c. 3p&2,=1 d. 2p&,=3 1.
2. 2. 0 the the stra strai% i%ht ht line liness ax+by ax+by+c +c= = and and bx+cy bx+cy+a +a= = are are parallel' then then which ! the !ll!win% is c!rrect: a. b2&#ac b. b2=ac c. b2+ac= d. a2=bc 21. !mp*te !mp*te the len%th len%th ! the lat*s rect*m rect*m ! the parab!la parab!la y 2& #y&12x&32=. a. 1 b. 12 c. 11 d. 16
d.
ind ind the area area ! the the hexa%!n hexa%!n 45D 45D7 7 !rm !rmed ed by 8!inin 8!inin% % the p!ints 4(1'#)' 5('&3)' (2'3)' D(&1'2)' 7(&2'&1) and (3'). a. 2# b. 2 c. 22 d. 1
1. ind the e,*ati! e,*ati!n n ! the parab!la parab!la wh!se axis is paralle parallell t! the x&axis and passes thr!*%h the p!ints (3'1)' (') and ("'&#). a. x2&2x&y= b. x2+2x+y= c. y2+2y+x= d. y2+2y&x= 11. 11. 4 p!int p!int (x'2) is e,*idista e,*idistant nt r!m the p!ints p!ints (&2') and (#'&). $he val*e ! x is a. 11/3 b. 2/3 c. 1/3 d. 6
12. 12. ind ind the the an%l an%lee betw betwee een n the the plan planes es 3x&y 3x&y+ +& &= = and and x+2y+2+2=. a. 62.# b. 2.#
22. ind ind the e,*ati!n e,*ati!n ! the circle circle havin% (1'2) (1'2) and (6'#) (6'#) as ends ! a diameter: a. x2+y2&16x+2y+2= b. x2+y2&1#x+2y+2= c. x2+y2&16x+"y+1= d x2+y2+1"x+2y+2= 23. 23. 4 para parab! b!li licc arc arc !ver !ver a t*nn t*nnel el !r !r a r!ad r!ad thr! thr!*% *%h h a m!*ntain is 2 t hi%h. $he width ! the arc 12 t r!m the t!p is 6 t. !w wide is the arc at the b!tt!m: a. "" t b. 6 t c. " t d. "# t
2#. ind ind the eccentricity eccentricity ! a hyperb!la hyperb!la wh!se transver transverse se and c!n8*%ate axes are e,*al in len%th. a. ."23 b. 1.2 c. 1.#1# d. 1.3#
2. ind ind the distance distance between between p!int (1''&3) (1''&3) r!m r!m the plane #x+y+"+33=. a. 3 b. # c. 2 d. 1
