SOLUTION: O is the center of the circle defined by x^2+y^2=169. Let P be the point in the first quadrant where x=5. Write the equation of the line tangent to the circle at point P and det

Algebra ->  Linear-equations -> SOLUTION: O is the center of the circle defined by x^2+y^2=169. Let P be the point in the first quadrant where x=5. Write the equation of the line tangent to the circle at point P and det      Log On


   



Question 846889: O is the center of the circle defined by x^2+y^2=169. Let P be the point in the first quadrant where x=5.
Write the equation of the line tangent to the circle at point P and determine the coordinates of P.

Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
The circle is centered at the origin, and the radius is 13 units. This is understood by reading from the standard form.

The y value for the given tangent point on the circle is y=sqrt%28169-25%29=12. This is for the point P(5, 12). The line for this radius is highlight_green%2812x=5y%29.

The question asked is essentially to find the equation of the line with slope -5%2F12 and contains the point (5, 12). You can plug the values into the point-slope form equation for a line and simplify into whatever form you want.

Starting that,...
highlight%28y-12=-%285%2F12%29%28x-5%29%29