The distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
(x₁,y₁), (x₂,y₂) - the coordinates of the points
[tex]P(5,35) \\
L(15,10) \\
F(9,25) \\ \\
\overline{PF} = \sqrt{(9-5)^2+(25-35)^2}=\sqrt{4^2+(-10)^2}=\sqrt{16+100}= \\
=\sqrt{116}=\sqrt{4 \times 29}=2\sqrt{29} \\ \\
\overline{LF}=\sqrt{(9-15)^2+(25-10)^2}=\sqrt{(-6)^2+15^2}=\sqrt{36+225}= \\
=\sqrt{261}=\sqrt{9 \times 29}=3\sqrt{29} \\ \\
\frac{\overline{PF}}{\overline{LF}}=\frac{2\sqrt{29}}{3\sqrt{29}}=\frac{2}{3}=2:3[/tex]
The answer is A.
