Equation of the line tangent to x^2+y^2=169? AT POINT (5,12)?

Question

Please show me the equation of the line tangent to this circle at point (5,12). I NEED THE STEPS TO DO THIS, AND I WOULD APPRECIATE A GENERAL FORMULA FOR SOLVING THIS AS WELL.

This needs to be solved without calculus. Show me how to solve the equation such that the ANSWER is "12y+5x-169=0"

Answer 1

ok because you know the line is tangent then you should be able to figure out that the line is perpendicular to the radius at that point

with the equation give you should know that the center is (0,0)

and slope of radius line to (5,12) is 12/5

since the tangent line is perpendicular to the radius it's slope is negative reciprocal of the slope of radius line

so slope of tangent line is -5/12

and now you can just plug and find the equation since you know the slope

12= -5/12 (5) + b

144= -25 + 12b

169=12b

b= 169/12

so your equation now is

y= -5/12x + 169/12

so to turn it into standard form just multiply by 12

12y= -5x + 169

12y + 5x - 169=0