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I am having some problem with my engineering maths project. i found out that the equation of circle is (x-h)^2 - (y-k)^2 = r^2 and that it is non-linear but do not know how to convert it to a matrix form to find the planar location. would appreciate it if someone would help or show the way to do it thanks the question is below.
a) A satellite can be represented by a circle, centred at (a1, b1). The distance between the
satellite and the GPS receiver is the radius of the circle, r1. The location of the GPS receiver
is (x, y). Write down an equation that relates the centre & radius of the circle with (x, y).
(b) GPS is based on satellite ranging, i.e. calculating the distances between a receiver and the
position of 3 satellites. The 2 other satellites are centred at (a2, b2) and (a3, b3). Their radii
are r2 and r3 respectively. Write down the corresponding equations that relate the centre &
radius with (x, y) for these 2 satellites.
(c) Explain whether equations from (a) and (b) are linear or non-linear. If they are non-linear,
algebraically simplify the equations to get a linear system in x and y.
(d) The location of the GPS receiver is on the circumference of each circle. It can be determined
by computing the intercept of the circles. Express the system of equations from (a) and (b) in
matrix form.
(e) From the data in the given table, determine the planar location (x, y) of a GPS receiver.
Circle Centre Radius
1 (-3,50) 41
2 (11,-2) 13
3 ( 13,34) 25
(f) Is matrix the only method to solve this problem, suggest an alternative method.