3A circle with centre 0 and the straight line intersect at the points $$ A(0 ; 5) $$ and $$ B(4 ; 3) $$. 2.3.1 Sketch the two graphs on the same set of axes. 2.3.2 Determine the equation of the circle. 2.3.3 Calculate the length of chord $$ A B $$. 2.3.4 Determine the equation of the straight line through A and B . 2.3.5 Calculate the co-ordinates of M , the midpoint of AB . 2.3.6 If $$ P(x ; y) $$ remains equidistant from the points A and B , prove that the equation of the locus of P is given by $$ y=2 x $$.

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The equation of the circle is $$ x^2 + y^2 = 25 $$. The length of chord $$ AB $$ is $$ 2\sqrt{5} $$. The equation of the line through $$ A $$ and $$ B $$ is $$ y = -\frac{1}{2}x + 5 $$. The midpoint $$ M $$ of $$ AB $$ is at $$ (2, 4) $$. The locus of point $$ P $$ equidistant from $$ A $$ and $$ B $$ is $$ y = 2x $$.

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