Test Key #5 - =~=~-~-~'j I MATH 150B Calculus II Test 5 1...

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? · ====================~ ~ ============================== ~ --~------~ .(.. 'j I • - - - J. ·- l ... •">- MATH 150B Calculus II Test# 5 Name \<7 .: ''"' G 1 i I . . -t 1. Find equations for (a) the tangent lines and (b) 3. !Classify the graph ofthe equation as a cirde ; r~ -2. · the normal lines to the hyperbola for the given parabola, ellipse, or a hyperbola. Give the . ' value of x. (20 points) 1 coordinates of center, vertices, foci, and the xz _ y2 = l, x = 6 I value of eccentricity ( e = c I a). (20 points) 9 x 2 + 4/ - 6x + 16y + 21 = 0 ~Q.VI- X-= 6 ..- "* - 'j ~~ \ , lj = ± S3 .. · ~ ~ GC ~ "- •' \? vJ\ s a{. :ll.. Ct u cl "j ~ .-1-elf'WIJ ""i.e v.h\\ ~""C\ \-A~o<~la.AA- o<A.,\. "vhi'YVVI .. ~ \tVl~ l Gtre- pc s:tf-; 11< Gt~c.\. ~ V\ ~i) "v01.; .+h-e_ Jl.<) c.t<-vWCl11 ~ C6/~) (;\ .... ~ c 6, -fi ).. . _ (ew<?s..e~ C\.v, Q..t\~r~ - " t:'- lu! ,\.Q. v-: v01...+• ~ :: - ~ _ L j ~I} -= 0 t:\. . cl '1 -= . .!... X. . ·}(z..+ 4 'j '"- 6 ;< -+ 1 6' ~ -t-l.. I ~ru q ({)( G\x 9. 8~ aW"'-- ~ o liL..\-.~ nf' r l!i>r"'f ~qMa rQ \hen?~ ... ~ slo ~ "1- +C\ Ill~ .e vv"\" "'Vl d ( \11) . ;::-) Q II\ r\ ' .~ l 0 ---r (,f'"" - 0 \1\. OVW'\cJt \.\At{ ( \f)w ) are . f:x -J) ·t t i1 tz) :::: I ( 0 \II r~) t (b l'i) \lh -~ - , Lr;;' : I q J8 2 2, l >... . ~ A '"' , '"~- l( -!T6- q, m~ ::- m~-::.- z.l6 ::.-z:- a.= z. / b ~l, · fher~~,., <:. == Jo. 2.-\l- ~<a f\'t (~;-f!!..)/ rn-t-= - · ~ · rs ~ -~ )'l.J -=--lit:: .3._::: lil (ew\-~\...-:: C~)c .. ) · ==- V>,.,-2-) ~) Tetl'\~ e•'* Li\1\t..t (lA~ {'Ott-~- . $\o~~ Jfw\M \1\kd : _ 28 + ·-, \(e-v+\'~ ~ t~± ~, ·&J :::: ( 3 ± 2./- 2.) 1*"{6~>: H-J8 · =-4()C. · w0 l l\7) Nt'Y~'V'I~ loH~-( I {C~j-2.))CI I · -Z)3 ) ~ 'a-i5i -=-?IT (')(-t} . Eoc~ :: L..e ±c, ..&..) -:::. ( 3 ±{$/ -2.) ~ At( '~-f3) : ~+V"S -= - 2.~3 (~~6) tA .n - s~ . J. ' ;) I[ { ( !:. ·t \S3' ~2)" ( 3 ·-J3 ·- 't)) -, (J 't~ ;s - ·- (X -b I . ,(";"' . . . z. 'If 'E:.c t e\1\.4-r•' c.,~ b- ~ E' :::: c /t'A :::- v3j 2 2. Two ~1croph~nes, 2 miles apa _t, record an 4. A wheel of radius a rolls along a line without 4 ·

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