Edexcel IALMathematicsGeneral Applications4 Marks
A circle C has equation x^2 + y^2 - 4x + 6y - 12 = 0. (b) The point P(5, -7) lies on C. Find the equation of the tangent to C at the point P.
- (b)The point P(5, -7) lies on C. Find the equation of the tangent to C at the point P.[4]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for finding the gradient of the radius CP using their centre from (a) and point P(5, -7).
- A1 for gradient of radius CP = -4/3.
- M1 for deducing the gradient of the tangent as 3/4 (using m1m2 = -1).
- M1 for using y - y1 = m(x - x1) with their perpendicular gradient and point P(5, -7).
- A1 for 4y - 3x + 47 = 0 (or equivalent, e.g., y = 3/4 x - 47/4, 4y = 3x - 47). Must be in the form of a linear equation.
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