ANALYTIC GEOMETRY REFRESHER SET 1.
Find the distance of the verte verte c!rve "#$%&$ ' () to the the *ine $ + ,) + - ' . a. 1.1 /. 1.,0 c. 1. d. 1.20
$.
There is a fied fied circ*e havin3 a radi!s radi!s of 0 4ith center at "(5-%. "(5-%. Find the the e6!ation of the c!rve connectin3 the centers of a** circ*es that are tan3ent to this fied circ*e and the #ais. a. &$ 7 - + $) ' 00 c. &$ + - + $) ' 00 /. &$ 7 - 7 $) ' 00 d. &$ + - 7 $) ' 00
,.
8hat 9ind 9ind of s)::et s)::etr)5 r)5 if an)5 an)5 does does the 3ra;h 3ra;h of ) ' &$ + 1 have< have< a. It is s)::etrica* 4ith res;ect to #ais. /. It does not have an) s)::etr). c. It is s)::etrica* 4ith res;ect to )#ais d. It is s)::etrica* 4ith res;ect to /oth aes.
(.
Co:;!te the the distance distance /et4een the directrices directrices of the the c!rve 2&$ + $0)&$ $0)&$ + 0( + $0) 7 (-1 (-1 ' . a. 10 /. 1$.0 c. 1 d. =.0
0.
A h);er/o*a h);er/o*a has the the e6!ation &$ + - + ()&$ 7 () () ' $05 find the center center of h);er/o*a. a. "-5(% /. "#-5(% c. "(5-% d. "#(5-%
.
T4o *ines *ines are re;rese re;resented nted /) the the e6!ations e6!ations #1>$ #1>$ ) ' 7 1 and ) ' :. Find the va*!e va*!e of : s!ch that the *ines 4i** /e ;ara**e*. a. 1$ /. #1$ c. d. #
=.
Find the *oc!s of a ;oint the the s!: of the s6!ares s6!ares of 4hose 4hose distances distances fro: "$5,% "$5,% and "#15#$% "#15#$% is ,(. ,(. a. &$ 7 )&$ + + ) + - ' c. &$ 7 )&$ 7 7 ) + - ' /. &$ 7 )&$ 7 + ) + - ' d. &$ 7 )&$ + 7 ) + - '
-.
Find the radi!s of the circ*e circ*e ;assin3 thro!3h the the ;oints ",5-% 5 "25% "25% 5 and "1,5#$% a. 2 /. 1 c. 1$ d.
2.
An e**i;s e**i;se e has an e6!ati e6!ation on of 2&$ 7 1)&$ 1)&$ ' 1((. 1((. a. 1.1 /. 1.11 c. 1.1-
d. 1.$=
1. In a three di:ensiona* s;ace !sin3 an )? coordinate coordinate s)ste:5 a *ine is connected /et4een "55=% and "(515%. @eter:ine the *en3th of the *ine. a. -.1$ /. 2.$= c. ., d. =.($ 11. 8hat is the e6!ation e6!ation of the *ine ;assin3 thro!3h thro!3h the ;oints of intersection intersection of the c!rves c!rves &$ 7 )&$ 7 1$ 7 ) 7 2 ' and &$ 7 )&$ 7 1- + () 7 $1 ' < a. #, 7 0) 7 ' c. , + 0) 7 ' /. , + 0) 7 ' d. #, + 0) 7 ' 1$. sin3 ;o*ar coordinates5 coordinates5 a ;oint is at "=5,-B%. Find the rectan3!*ar rectan3!*ar coordinates. coordinates. a. "(.=5 0.$% /. ".(5,.2% c. "0.05(.,% d. ".$5 (.% 1,. ECE DOAR@ @eter:ine @eter:ine D s!ch that , 7 $) + = ' is ;er;endic!*ar ;er;endic!*ar to $ + D) 7 $ ' . a. 0 /. ( c. , d. $ 1(. Find the area of the trian3*e trian3*e 4hich the *ine $ + ,) 7 ' for:s 4ith the coordinate coordinate ais. a. , /. ( c. 0 d. $ 10. 8hat is the s*o;e of the *ine *ine 4hich is defined /) the e6!ation e6!ation () ' , 7 1. a. 1 /. .=0 c. , d. ( 1. Find the e6!ation of the ;*ane thro!3h thro!3h "$515#,% ;ara**e* to the ;*ane ,7()7 ,7()7?'(< ?'(< a. , + () + ? ' $ /. , 7 () 7 ? ' = c. , 7 () 7 ? ' #= d. , 7 () 7 ? ' $ SITATION 1 The e6!ation of the ;*ane ;assin3 thr! ;oints "05(51% 5 "(5#$5#,% and "550% is e;ressed as >A 7 )>D 7 ?>C ' 1. 1=. Find the va*!e va*!e of D. a. #$>,
/. #1>,
c. $>,
d. 1>,
1-. Find the va*!e va*!e of C. a.
/. 1>,
c. #1>$
d. #1>,
12. Find the the e6!ation e6!ation of the ;*ane. ;*ane. a. $ $ + ,) 7 (? ' # #$ $ /. # #$ $ 7 ,) 7 (? ' #$ c. $ + ,) 7 ( (? ? ' $
d. $ 7 , ,) ) + (? ' $
$. Find the circ!:ference circ!:ference /o!nded /o!nded /) the c!rve &$ + 1 7 )&$ 7 1) 7 $0 ' a. 1 /. $0 c. 0 d. 1$0
$1. He co:;*eted the so*!tion of the *oc!s of a circ*e. a. Hi;;arch!s /. E!c*id c. A;;o*oni!s
d. )tha3oras
$$. Ho4 :an) ;oints of intersection /et4een the c!rve &$ # ()&$ 7 $ 7 -) 7 1 ' and the *ine $) ' 7 ,. a. /. 1 c. $ d. Cannot /e deter:ined SITATION $ For the c!rve (&$ + ()&$ + ,$ 7 1) 7 ,2 ' 5 $,. Find the center. a. "(51%
/. "(5
%$c. "$5(%
d. "15(%
$(. Find the e6!ation of the ;rinci;a* ais. a. ' $ /. ) ' $
c. ' #$
d. ) ' #$
$0. The fo**o4in3 c!rve is c*assified as a. H);er/o*a /. E**i;se
c. ara/o*a
d. Circ*e
$. The ;oints ",51%5"05$%5"1050%5 and "1=5% is for:ed in a sha;e of a. ara**e*o3ra: /. Tra;e?oid c. Rectan3*e d. ite $=. Find the ) coordinate of *at!s rect!: ;oints of the c!rve ' )&$ + -). a. =>$ ). 2>$ c. Doth d. None $-. Find the #coordinate of the foc!s of the c!rve &$ ' #1$). a. /. 1$ c. ,
d. #(
$2. @eter:ine the *en3th of the *at!s rect!: of the c!rve r ' (>"1#sinJ% . a. ( /. 1 d. d. ,. A s!rface 4hose e6!ation is of the second de3ree is ca**ed a. *ane S!rface /. Linear S!rface c. K!adric S!rface
d. o*ar S!rface
,1. A :ovin3 ;oint is e6!idistant fro: the ;oint "a55% and the *ine 7 a ' 5 ) ' . Find the va*!e of ?&$. a. /. (a) c. (a d. (a? ,$. The fo**o4in3 ;ossi/*e ;ara:etric e6!ations ECET a. ' t /. ) ' t 7 c. ' t 7 1
d. ) ' t&$ 7 $t 7 =
,,. Find the *ine tan3ent of )&$ ' #, at "#15#$%. a. + $) ' , /. , + ) ' $ c. $ 7 ,) ' #1
d. 7 $) ' ,
,(. State the 6!adrant in 4hich the coordinate "105#$% *ies. a. I /. II c. III
d. I
,0. Given the e6!ation of the ;ara/o*a )&$ + - + () + $ ' 5 Find the *en3th of *at!s rect!:. a. $ /. ( c. d. ,. If the distance /et4een ;oints "$525(% and "$525?% is 15 4hat is the va*!e of ?< a. # /. c. d. None ,=. If t4o ;oints in the sin3*e di:ensiona* coordinate have coordinates 1 and =5 4hat is the coordinate of a ;oint on the *ine in 4hich is t4ice as far as 1 as fro: =< a. , /. ( c. 0 d. ,-. Find the eccentricit) of the e**i;se havin3 an e6!ation of (&$ 7 2)&$ ' 1,. a. $ /. , c. .=0 d. .00 ,2. Find the e6!ation of the dia:eter of the e**i;se (&$ 7 )&$ ' 1 4hich a** /isects a** chords havin3 e6!a* s*o;e of 1>$. a. - 7 ) ' /. 7 -) ' c. Doth d. None (. 8hat is the an3*e in de3rees /et4een the *ine , + $) + ( ' and the #ais< a. $$.0B /. ,-.=B c. 0.,B d. =(.0B (1. 8hat is the center of the conic in the c!rve ) + 7 $) 7 , ' < a. "$51% /. "#$51% c. "$5#1%
d. "#15#
%$($. Find the e6!ation of the as):;tote in the c!rve $) ' &$ 7 ,. a. ' $ /. ) ' $ c. '
d. ) '
(,. @eter:ine the c)*indrica* coordinates of the ;oint 4hose rectan3!*ar coordinate is "1>0 5 1$>0 5 ,%. a. "#(5#,.-=B5,% /. "(5,.-=B5,% c. "050,.1,B5(% d. "050,.1,B5(% ((. Ho4 far fro: the #ais is the foc!s of the h);er/o*a &$ + $)&$ 7 ( 7 () 7 ( ' < a. 1.0= /. $.=, c. ,.1$ d. 0.1 (0. The corners of a 6!adri*atera* are "(5%5"1$5(%5"15-% and "(5(%. Ho4 far is the centroid fro: the )#ais< a. .$$ /. .-= c. =.$ d. =.(. The se3:ent fro: "#15(% to "$5#$% is etended three ti:es its o4n *en3th. @eter:ine the ter:ina* ;oint< a. "115#$% /. "#1-51$% c. "#15#-% d. "=512% (=. Find the distance fro: the ;oint "$5,% to the *ine , 7 () 7 2 ' . a. $.= /. $.( c. 0.( d. .SITATION , A circ*e is descri/ed a*3e/raica**) /) the e6!ation &$ 7 )&$ + 7 -) 7 $1 ' . (-. @eter:ine the center of the circ*e. a. ",5#(% /. "#(5,%
c. "#,5(%
d. "#,5#(%
(2. Find the ;eri:eter of the circ*e. a. $ /. ,
c.
d. (
0. Find the area of the circ*e. a. $ /. ,
c.
d. (
