Equation of circle and straight line in senior two mathematics.

The tangent of (1) circle o from point p is y=kx-5k(x=5 is not tangent to circle o).

Center O (0 0,0), radius r=4.

(-5k/( 1+k^2))^2= 16

K= plus or minus 4/3

So y=4/3x-20/3 or y=-4/3x+20/3 is tangent to the circle O.

Let the tangent point be a.

PA= radical number (po 2-OA 2) = radical number (5 2-4 2) = 3.

(2)

Let A(x 1, y 1), B(x2, y2), and the straight line AB:y=kx-5k(x=5 does not intersect with the circle o).

y=kx-5k

x^2+y^2= 16

= & gt( 1+k^2)x^2- 10k^2x+25k^2- 16=0

x 1+x2= 10k^2/( 1+k^2)

y 1+y2 = kx 1-5k+kx2-5k

=k(x 1+x2)- 10k

=- 10k/( 1+k^2)

Midpoint C (5k 2/(1+k2), -5k/( 1+k 2))