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
2. The intersecting line becomes a tangent if the radical equals zero. And exactly there you'll find the given condition.