A circle with centre $$$C$$$ has equation $$$(x-8)^{2}+(y-4)^{2}=100$$$. The two tangents touch the circle at $$$A$$$ and $$$B$$$. Find the equation of the line $$$A B$$$, giving your answer in the form $$$y=m x+c$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_13 Year：2020 Question No：11(c)

Answer:

Gradient, $m$, of $C T=-\frac{1}{7}$
Attempt to find mid-point (M) of $C T$
Equation of $A B$ is $y-5=7(x-1)$
$y=7 x-2$

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.)

Answer:

Knowledge points:

Solution:

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