Question

Find the equation of the circle with center at (2,5) and tangent to the line 2x + 3y = 5

Answer 1

Someone on here will be able to do this better than I but I can get you started

Answer 2

we know the general form of a circle is
\[(x-h)^2 + (y - k)^2 = r^2\]

Answer 3

mmhmm

Answer 4

where h and h are the x and y coordinates

Answer 5

Like this?

Answer 6

so therefore h=2 k = 5

Answer 7

im thinking getting the slope of the tangent line then getting its perpendicular slope to get the slope of radius

Answer 8

yes

Answer 9

but how will i find the length then

Answer 10

intersection?

Answer 11

yes

Answer 12

but how do i find the equation of the radius

Answer 13

figure out a "b" that satisfies the center

Answer 14

\(2x + 3y-5 = 0\) (General form)

-A/B to find the slope

-2/3

Answer 15

a "b" that satisfies the center?

Answer 16

then use distance from center point to intesection

Answer 17

lol there might be an easier way tho so stayed tuned

Answer 18

hmm maybe i can use \[\frac{y_2 - y_1}{x_2 - x_1} = -2/3\]

Answer 19

\[\frac{y_2 - 5}{x_2 - 2} = -2/3\]

Answer 20

The radius is perpendicular, so the sole of the radius is 3/2

Now find the equation of the radius, passing through (2,5)

f(x) = mx+b
5=3/2(2)+b
5=3+b
b=5-3=2

So equation of the radius is

\(f(x)=\frac{3}{2}x+2\)

Answer 21

lol i thought when you said slope is -a/b that was the perpendicular already -_-

Answer 22

you should stop beating around the bush :P

Answer 23

Now find the point right there:


We have the tangent and the equation of the radius
\(2x + 3y = 5\)
and
\(y=\frac{3}{2}x+2\)

:P Sir lgba, http://openstudy.com/users/zepp#/updates/4fa3474fe4b029e9dc34125e