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 :)
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Does anyone know? I would really appreciate some help.
well, the circle.... hold one, lemme make a quick picture
@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.
right, you get that slope, then you use the "negative reciprocal" for the perpendicular :)
That's right jDoe
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.
do you need CPR? or maybe electrical shocks? dunno :)
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
@jdoe0001 I'm still confused
@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?
Thanks I understood the problem now. The answer I got is y= -3/4x+25/4