The diagram shows a circle with centre $$$A$$$ passing through the point $$$B$$$. A second circle has centre $$$B$$$ and passes through $$$A$$$. The tangent at $$$B$$$ to the first circle intersects the second circle at $$$C$$$ and $$$D$$$. The coordinates of $$$A$$$ are $$$(-1,4)$$$ and the coordinates of $$$B$$$ are $$$(3,2)$$$. Find the equation of the tangent $$$C B D$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_11 Year：2020 Question No：9(a)

Answer:

$m_{A B}=\frac{4-2}{-1-3}=-\frac{1}{2}$
Equation of tangent is $y-2=2(x-3)$

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.)

Answer:

Knowledge points:

Solution:

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