Work out the equation of the tangent to a circle of centre [0,0] at the point [4,3]

We know that: (1) the radius of the circle to the point [4,3] is perpendicular to the tangent line, (2) if two lines are perpendicular, their gradients are negative reciprocals of each other, and (3) the formula for a straight line is y = mx + c. The radius gradient is equal to 3/4, so the tangent gradient is -4/3. Substituting m, y and x at [4,3] into the straight line formula gives c as 25/3. Therefore, the equation of this tangent line is y = (-4/3)x + (25/3).