+280 Find all points (x, y) that are 5 units away from the point (2, 7) and that lie on the line \(2x + y = 13\)
+15000 Find all points (x, y) that are 5 units away from the point (2, 7) and that lie on the line 2x + y = 13
Helo ABJelly!
\(f_1(x)=\pm\sqrt{5^2-(x-2)^2}+7\\ f_2(x)=-2x+13\\ f_1(x)=f_2(x)\\ \pm\sqrt{5^2-(x-2)^2}+7=-2x+13\\ \sqrt{5^2-(x-2)^2}\ ^2=(-2x+6)^2\\ 5^2-(x-2)^2=4x^2-24x+36\)
\(25-x^2+4x-4=4x^2-24x+36\\ 5x^2-28x+15=0\\ x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ \color{blue}x\in \{\frac{3}{5},5\}\\ \color{blue}f_1(x)=11.8\\ \color{blue}f_2(x)=3\)
The points we are looking for are (0.6,11.8) and (5,3).
!
+15000 Find all points (x, y) that are 5 units away from the point (2, 7) and that lie on the line 2x + y = 13
Helo ABJelly!
\(f_1(x)=\pm\sqrt{5^2-(x-2)^2}+7\\ f_2(x)=-2x+13\\ f_1(x)=f_2(x)\\ \pm\sqrt{5^2-(x-2)^2}+7=-2x+13\\ \sqrt{5^2-(x-2)^2}\ ^2=(-2x+6)^2\\ 5^2-(x-2)^2=4x^2-24x+36\)
\(25-x^2+4x-4=4x^2-24x+36\\ 5x^2-28x+15=0\\ x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ \color{blue}x\in \{\frac{3}{5},5\}\\ \color{blue}f_1(x)=11.8\\ \color{blue}f_2(x)=3\)
The points we are looking for are (0.6,11.8) and (5,3).
!
