Question

Consider the circle of the radius 5 centered at (0,0). Find an equation of the line tangent to the circle at the point (3,4) in slope intercept form. Thanks :)

Answer 1

Does anyone know? I would really appreciate some help.

Answer 2

well, the circle.... hold one, lemme make a quick picture

Answer 3

Do you know what the equation for the circle is?

Answer 4

(x-h)^2+(y-k)^2=r^2

Answer 5

as you can see from the picture above, you have a line, you have 2 points, the origin and the given (3, 4)
using that, get the slope for the blue line of 5 units long

Answer 6

what the ?

Answer 7

jdoe, no

Answer 8

from the picture there hehe

Answer 9

@joselin12 Find out the equation for the line going from the origin to the point, then the line perpendicular to that will be the slope of your tangent line.

Answer 10

right, you get that slope, then you use the "negative reciprocal" for the perpendicular :)

Answer 11

That's right jDoe

Answer 12

you don't even need to find the equation of the radius from (0,0) to (3, 4). Just find the slope.

The radius and tangent intersect at right angles, meaning the tangent is perpendicular to the tangent.

so of m = slope of radius, -1/m will be the slope of the tangent.


then you can find the equation of the tangent.

Answer 13

joselin12 confused?
do you need CPR? or maybe electrical shocks? dunno :)

Answer 14

so the slope of the radius is

m = (4 - 0)/(3 -0)

so the slope of the radius is 4/3

then the slope of the tangent is -3/4

using the slope intercept form of a straight line

the equation is

y = -3/4 x + b

to find b, substitute x = 3 and y = 4 and solve for b

Answer 15

@jdoe0001 I'm still confused

Answer 16

@joselin12 see the picture above... you have a line from the origin to the edge of the circle at (3, 4)

as FutureMathProfessor and campbell_st suggested, get its slope
do you know how to find the slope from 2 points?

Answer 17

Thanks I understood the problem now. The answer I got is y= -3/4x+25/4

Answer 18

yw