Given:
The equation of a circle is

A tangent line l to the circle touches the circle at point P(12,5).
To find:
The gradient of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is

Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is


We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.



Therefore, the gradient or slope of the tangent line l is
.
I'll just help quickly with a couple of expressions that are equivalent.
3(m+5+9m)
If you solve it out, you get 3m+15+27m.
Simply the expression to get 30m+15.
You can regroup to make another expression 5(6m+3) which is also equal.
ANSWER

EXPLANATION
From the Pascal's triangle,
The coefficients are :
1, 5, 10,10, 5,1
Because of the negative sign, the expansion will alternate sign.

We now put y=5 into the expansion to get,

