Show that 5n+10 gives the correct slope for line tangent to circle with radius 13 @ (-5,12)?

Question

1)Find an integer, x, greater than 4 where the sum of x consecutive integers is divisible by x

2) Show that the equation above gives the correct slope for the line tangent to a circle with a radius of 13 at the point (-5,12)

So I'm thinking, the circle's center is at (0,0) because then the point of tangency will be (-5,12) exactly...But I don't know what to do

For #1, I got 5n+10....is that right or wrong

Answer 1

q1

let the numbers be n+1 till n+x.

then the sum is

= nx + x(1+x)/2

when the sum is divided by x, it will become n + (1+x)/2.

so if (x+1) has to be even, then x must be an odd integers, greater than 4.

x = 5, or any odd integers greater than 5.

q2

m = -1/(12/-5) = 5/12

point of tangency is (-5,12), yes.

y - 12 = 5(x + 5)/12

y = 5x/12 + 169/12