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In an orthonormal system, you're given the following: Point P(1,2)
Lina a=cartesian eqn:4x-3y+6=0
Line b=parametric eqns:x=-5+3&
y=-& (real n°)
Circle z=cartesian eqn:x²+y²-2x-3=0

(a)Calculate the angle between lines a an b

(b)Calculate the coordinates of the point of intersection of lines a and b

(c)Calculate the distance from P to line b

(d)Find the centre C and the radius r of circle z

(e)Calculate the cartesian eqn of the tangent t to the circle z at the point T(-3/5,6/5) Show that this tangent is line a

(f)M,P,N are,respectively,the points on t and z having the same x coordinates as C. Show that MT²=MP*MN


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