This is a problem of intersection. So, we have two equations, first of all we have a straight line and the second equation is a circle with ratio equal to 1. Therefore, in a mathematical language this is established as follows:
(1)[tex]y = \frac{-7x}{4}[/tex]
(2)[tex]x^{2}+y^{2}=1[/tex]
We introduce (1) into (2):
[tex]x^{2}+(\frac{-7x}{4})^{2}=1[/tex]
[tex]x^{2}+\frac{49x}{16}^{2}=1[/tex]
[tex]65x^{2}=16[/tex]
There are two values, namely:
[tex]\left \{ {{x_{1} = +0.4961 } \atop {x_{2} = -0.4961 }} \right.[/tex]
Then, substituing these values in the first (1) equation, we find:
[tex]\left \{ {{y_{1} = -0.8681 } \atop {y_{2} = +0.8681 }} \right.[/tex]
Finally, the points are two:
[tex]P_{1}=(0.4961,-0.8681)[/tex]
[tex]P_{2}=(-0.4961,0.8681)[/tex]
