Which of these is the equation for a line tangent to the circle x^2 + y^2 = 20 at point (2, -4)?

i got 2x+sq20 correct or no?

Question

Which of these is the equation for a line tangent to the circle x^2 + y^2 = 20 at point (2, -4)?

i got 2x+sq20 correct or no?

freckles · Answer

I would first find y' given x^2+y^2=20

freckles · Answer

then use the point (2,-4) to find the slope to the circle equation x^2+y^2=20 @ (2,-4)
then use the point ...

point slope form for a line is
$$y-y_1=m(x-x_1) \ \text{ we are given } (x_1,y_1)=(2,-4) \ y-(-4)=m(x-2) \ y+4=m(x-2) \ y=m(x-2)-4 $$
you need to find m

freckles · Answer

m is y' evaluated at (2,-4) 
(this is the slope at (2,-4))

freckles · Answer

can you find that?

anonymous · Answer

find the slope?

anonymous · Answer

or what do i find?

freckles · Answer

do you not know calculus?

freckles · Answer

If you don't we can do this algebraically

anonymous · Answer

its algebra class :p

freckles · Answer

ok y' is a calculus thing

freckles · Answer

so here we would have to look at this:
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say this is our circle with center (0,0) and radius sqrt(20)

freckles · Answer

|dw:1418530691761:dw|
a line that is drawn tangent to a circle 
is perpendicular to the radius I have drawn