Math Problem.... Need Help?

Question

Consider the circle with a radius of 5 and centered at (0,0). Find the equation of the line tangent to the circle at the point (3,4).

I was assigned this for school and I have no idea how to do it... Any help would be huge.. Thanks

Answer 1

Circle's formula is x^2+y^2=25. Solve for y. --> y=sqrt(25-x^2)

Take the derivative. y'=(1/2)((25-x^2)^(-1/2))(-2x)=-x/(sqrt(...

Plug in x=3. -3/(sqrt(25-3^2))=-3/(sqrt(16))=-3/4

This is the slope of the tangent line at (3,4). We have y=(-3/4)x+b.

Plug in (3,4) to find b.

4=(-3/4)(3)+b

4=-9/4+b

b=25/4

y=(-3/4)x+25/4