The equation of a circle with centre $$\(C\)$$ is $$\(x^{2}+y^{2}-8 x+4 y-5=0\)$$. The tangents to the circle at $$\(P\)$$ and $$\(Q\)$$ meet at $$\(T\)$$. Find the coordinates of $$\(T\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_12 Year：2020 Question No：11(d)
Answer:
Gradient of tangent at \(Q=-\frac{3}{4}\) by symmetry
(FT from part (b))
Eqn of tangent at \(Q\) is \(y-2=-\frac{3}{4}(x-7)\) or \(4 y+3 x=29\)
\(T\left(4, \frac{17}{4}\right)\)
(FT from part (b))
Eqn of tangent at \(Q\) is \(y-2=-\frac{3}{4}(x-7)\) or \(4 y+3 x=29\)
\(T\left(4, \frac{17}{4}\right)\)
Knowledge points:
1.3.4 use algebraic methods to solve problems involving lines and circles (Including use of elementary geometrical properties of circles, e.g. tangent perpendicular to radius, angle in a semicircle, symmetry.) (Implicit differentiation is not included.)
Solution:
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