I've come across this question and was wondering how to prove it, particularly since the book from which the question has come from assumes no knowledge of calculus.

The equation of a straight line is y=ax+b, where a and b are constants.

The equation of a circle is: x^2 + y^ = 64.

The straight line is a tangent to the circle.

Prove that a^2 + 1 = b^2 / 64

Any ideas?