Additional Mathematics – Coordinate geometry of the circle | e-Consult

Write each circle in centre–radius form.

Circle E: \((x-3)^2+(y+4)^2=16\) → centre \(E(3,-4)\), radius \(4\).

Circle F: \((x+2)^2+(y-1)^2=8\) → centre \(F(-2,1)\), radius \(\sqrt{8}=2\sqrt{2}\).

Distance between centres:

\[

EF=\sqrt{(3+2)^2+(-4-1)^2}= \sqrt{5^2+(-5)^2}= \sqrt{50}=5\sqrt{2}.

\]

Sum of radii: \(4+2\sqrt{2}\approx 6.83\).

Difference of radii: \(|4-2\sqrt{2}|\approx 1.17\).

Since \(EF=5\sqrt{2}\approx 7.07\) is greater than the sum of the radii, the circles do not meet.

Therefore there is no common chord.