SOLUTION: a circle defined bythe equation (x-6)+(y-9)=34 is tangent to a line at the point 9.4 what is the equation of the line

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Question 1132240: a circle defined bythe equation (x-6)+(y-9)=34 is tangent to a line at the point 9.4 what is the equation of the line
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe you mean at the point (9,4).
that would be the point whose x-value is 9 and y-value is 4.

the center of the circle is at he point (6,9).

i believe you also meant that the equation if (x-6)^2 + (y-9)^2 = 34

the tangent to the circle at the point (9,4) will be perpendicular to the radius of the circle that intersects that point.

the equation for the radius of the circle that goes through the point (9,4) is:

y = -5/3 * x + 19

the equation for the line tangent to the circle at the point (9,4) is:

y = 3/5 * x - 7/5

the graph of the circle and line representing the radius of the circle and the line tangnt to the circle at the point (9,4) is shown below:

$$$

the circle is red.
the radius is blue.
the tangent to the circle perpendiular to the radius at the point (9,4) is green.

you should already know how to find the equation of the line through two points so i didn't get into how to do that.

if you need instructions on that, you can view the reference below.

there are also instructions on the equation of a circle, in case you're not familiar with that.

https://www.mathsisfun.com/algebra/line-equation-2points.html

https://www.purplemath.com/modules/sqrcircle.htm