The coordinates of the points $A$ and $B$ are $(-1,-2)$ and $(7,4)$ respectively. Find the equation of the tangent, $$\(T\)$$, to circle $$\(C\)$$ at the point $$\(B\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_11 Year：2020 Question No：10(b)
Answer:
Gradient from \((3,1)\) to \((7,4)=3 / 4\) (this is the normal)
Gradient of tangent \(=-\frac{4}{3}\)
Equation is \(y-4=-\frac{4}{3}(x-7)\) or \(3 y+4 x=40\)
Gradient of tangent \(=-\frac{4}{3}\)
Equation is \(y-4=-\frac{4}{3}(x-7)\) or \(3 y+4 x=40\)
Knowledge points:
1.3.1 find the equation of a straight line given sufficient information
1.3.2 interpret and use any of the forms in solving problems (Including calculations of distances, gradients, midpoints, points of intersection and use of the relationship between the gradients of parallel and perpendicular lines.)
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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