Question

Write the equation of the circle. The circle is tangent to the line 3x - 4y = 24, and the center is at (1,0).

help, please :))

Answer 1

your job is to find the radius of the circle, aka the distance between the line
\[3x-4y=24\] and the point \((1,0)\)
do you know how to do that?

Answer 2

distance between the perpendicular line and the center of the circle. there's a formula for that right?

Answer 3

there may be but i don't know it
your line has slope \(\frac{3}{4}\) perpendicular line with l have slope \(-\frac{4}{3}\) so you can find the equation of the line with slope \(-\frac{4}{3}\) through \((1,0)\) and see where it intersects the line
\[3x-4y=24\]

Answer 4

y-0 = -4/3 (x-1) ??

Answer 5

yes

Answer 6

oh it also looks like you can use a formula directly
if the line is
\[ax+by=c\] then the distance between the line and a point not on the line is
\[\frac{|ax+by+c|}{\sqrt{a^2+b^2}}\] it may be easier to use this

Answer 7

Oh. That's what I did at first but my classmate corrected me and everything suddenly confused me -_-"

Answer 8

same answer in any case you get
\[\frac{|4\times 1-3\times 0+24|}{\sqrt{3^2+4^2}}\]

Answer 9

y-0 = -4/3 (x-1)
Y = -4/3X + 4/3 ?

Answer 10

i like this method better but yes you are right, and then you would have to find where the lines intersect and then find the distance. but this formula gives it directly

Answer 11

i get the distance is \(\frac{20}{5}=4\) so it is snappy

Answer 12

and basically you are done, right?

Answer 13

yeah :)
thank you!

Answer 14

yw