The equation of the tangent..?

Question

The equation of the tangent line to the curve x^2 + y^2 = 169 at
the point (5, -12) is?

Answer 1

Use implicit differentiation: 2x dx/dx +2y dy/dx=0
or dy/dx=-x/y. So at the point (5,-12), the slope of the tangent is 5/12. Finally, use the slope intercept fomula:
y+12=(5/12)(x-5). Thats it.

Answer 2

x^2 + y^2 = 169 describes a circle centered at the origin with a radius of sqrt(169) = 13.

The tangent at point 5,-12 will be perpendicular to the radius to that point.

we know the slope of the radius is:
(y-0)/(x-0) = -12/5

So the slope of the tangent is -1/slope of radius = 5/12

let the tangent be y = mx + b
we know m is 5/12, ie y = 5x/12 + b

for point (5,-12), -12 = (5*5)/12 + b
solve for b,
and plug it back to the equation and that will give you your tangent.

Answer 3

tangentttttt