Question

Find an equation of the tangent line to the circle: x^2+y^2=25 at point (-3,4). then graph the line together with the circle.

Answer 1

in order to graph equations, you need to solve them for y. To graph x^2+y^2=25 plot y=sqrt (25-x^2) and y=-(sort)25-x^2

Answer 2

I REALLY REALLY NEED QUICK FAST HELP GUYS!

Answer 3

to get equation of line, we need slope and a point on that tangent
point is givn, do u know how you can get slope ??

Answer 4

x^2+y^2= 25
differentiate this w.r.t x, what u get ?

Answer 5

whats w.r.tx?

Answer 6

i'm solving for y right now and got y=sqrt(25-x^2)

Answer 7

now i'm finding the first derivative respect to x right?

Answer 8

w.r.t x means with respect to x :P
ok, yes for slopee, you'll need dy/dx at x=-3

Answer 9

x^2+y^2 is a circle with centre as origin and radius = sqrt 25 = 5

Answer 10

**x^2+y^2=25

Answer 11

right~ ok so far so good!

Answer 12

x^2+y^2= 25 differentiate this w.r.t x, what u get ?

Answer 13

-x/sqrt25-x^2 = y' no? yes?

Answer 14

there was no need to isolate 'y' for differentiating.....
you could've implicit differentiated x^2+y^2 = 25
to get
2x + 2y (dy/dx) = 0

got this ??
now isolate dy/dx from that

Answer 15

derivative of y^2 will be 2y (dy/dx) because of chain rule

Answer 16

so what I did was wrong?

Answer 17

not incorrect, but not required...

Answer 18

you'll get same slope with what you have done and inplicit differentiation...
why not take an easier way when you have it :)

Answer 19

ok.

Answer 20

so then its -2x/2y right?

Answer 21

yes!
dy/dx = -x/y
and slope of tangent will be dy/dx at x =-3, y =4

so, slope = m = -(-3)/4 = ... ?
getting this ?

Answer 22

yup so far!

Answer 23

now you have slope and a point also on the tangent
can you find the equation ??

Answer 24

use, y-y1 = m (x-x1)

Answer 25

right but how do I plot the circle when the plots are like y= sqrt 25-x^2?

Answer 26

as i said, \(x^2+y^2 =r^2 \)
is a circle with origin as centre (0,0) and radius = r
here, r=5

Answer 27

why are they giving me two y's?

Answer 28

ok so what if I know the radius? what does that imply?

Answer 29

to plot a circle, you only need centre and radius!
like circle with radius = r and centre as origin will be plot as