Question

Find an equation of the line that is tangent to the circle x^2 +y^2=25 at the point p(3,4)

Answer 1

You know derivative?

Answer 2

Ok lets find the slope of the line from the center of the circle to the point w/c is given.
What do u think it would be?

Answer 3

so it will be (0,0) and (3,4)?

Answer 4

\[m_{\perp} =\frac{4-0}{3-0}\]

Answer 5

so the slope will be 4/3 isn't

Answer 6

It is the slope of the radius to the point (3, 4)

Answer 7

Now find the slope w/c is perpendicular to the above slope.
Tell me what it would be?

Answer 8

-3/4

Answer 9

YEP now u have the slope and the point. what will be the line?

Answer 10

so we substitute it in the point-slope formula? y-4=-3/4(x-3)

Answer 11

Great, done.

Answer 12

but why do we need to make the slope be perpendicular?

Answer 13

w/c slope?

Answer 14

oh, ok thankyou very much

Answer 15

well come