This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Step 1: Determine the coordinates of the centre O and the point of tangency A. From the diagram 3.4, the centre of the circle is O(0, -1). The point where the tangent touches the circle is A(9, -1). Step 2: Calculate the gradient of the radius OA. The radius OA connects the centre O(0, -1) and the point of tangency A(9, -1). The gradient m_OA is given by the formula m = (y_2 - y_1)/(x_2 - x_1). m_OA = (-1 - (-1))/(9 - 0) = (-1 + 1)/(9) = (0)/(9) = 0 Since the gradient of the radius OA is 0, the radius OA is a horizontal line. Step 3: Determine the equation of the tangent PQ. The tangent line PQ is perpendicular to the radius OA at the point of tangency A. If the radius OA is a horizontal line, then the tangent PQ must be a vertical line. A vertical line passing through a point (x_1, y_1) has the equation x = x_1. The tangent PQ passes through point A(9, -1). Therefore, the equation of the tangent PQ is x = 9. The equation of the tangent PQ is x = 9. Drop the next question.