ch 10

Question 1

how to find tangent line to parametric curve

Answer 1

find dy/dx
plug in x or y to solve for t
cancel t’s by plugging it into x or y equation
plug t into dy/dx equation and write in y=mix+b

Question 2

parabola

Answer 2

one squared

Question 3

circe=le

Answer 3

exactly the same

Question 4

ellipse

Answer 4

same sign but different h

Question 5

hyperbola

Answer 5

different signs

Question 6

area of a parametric curve

Answer 6

s = sqrt (dx/dt)^2 + (dy/dt)^2

Question 7

polar to rectangular

Answer 7

rcostheta, rsintheta

Question 8

rectangular to polar

Answer 8

(+- sqrt x^2+y^2, arctan(y/x))

Question 9

find value on theta w point on curve with shortest distance from pole

Answer 9

find dr/dtheta
and set = 0
find critical points and use that and end points
plug everything into r and see shortest

Question 10

area of a sector

Answer 10

a = 1/2 int r^2dr

Question 11

circle equation

Answer 11

r=asintheta r=acostheta

Question 12

cardioid equation and features

Answer 12

r= a+_bcostheta
r=a+_bsintheta
heart shaped
a/b=1

Question 13

limacon w inner loop

Answer 13

r=a+_ bcostheta
r=a+_bsintheta
inner loop
a/b <1

Question 14

dimpled limacon

Answer 14

r=a+_bcostheta
1<a/b<2

Question 15

convex limacon

Answer 15

a/b>2

Question 16

rose curves

Answer 16

r=acosbtheta

Question 17

lemniscate

Answer 17

r^2 = a^2sin2theta

Question 18

finding tangent to polar curve
equation

Answer 18

dy/dx =
(r’thetasintheta + rthetacostheta)
______________________________________
(r’thetacostheta + r theta sin theta)

x = rcostheta. y = rsintheta

Question 19

tangent at the pole

Answer 19

dy/dx = tan theta

Question 20

arc length of polar curve

Answer 20

s = int sqrt (theta)^2 + f’theta^2