The centre of a circle is the point with coordinates (−1, 3) The point A with coordinates (6, 8) lies on the circle - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 1

The gradient of the tangent line (m_t) is the negative reciprocal of the gradient calculated above:

$m_t = -\frac{1}{m} = -\frac{1}{\frac{5}{7}} = -\frac{7}{5}$

Now using the point-slope form of the line equation, which is: $y - y_1 = m_t (x - x_1)$ Given point A (6, 8):

$y - 8 = -\frac{7}{5}(x - 6)$

Simplifying this:

1. Distributing: $y - 8 = -\frac{7}{5} x + \frac{42}{5}$
2. Rearranging to standard form: $y = -\frac{7}{5} x + \frac{42}{5} + 8$ $y = -\frac{7}{5} x + \frac{42}{5} + \frac{40}{5}$ $y = -\frac{7}{5} x + \frac{82}{5}$
3. Multiplying everything by 5 to eliminate the fraction: $5y = -7x + 82$ $7x + 5y - 82 = 0$

Thus, the equation of the tangent line is:

$7x + 5y - 82 = 0$

Where a = 7, b = 5, and c = -82, fulfilling the requirement that a, b, and c are integers.