Answer:
The line does not intersect the curve
Step-by-step explanation:
Assuming that we are looking for the points of intersection of
[tex] {x}^{2} + {y}^{2} = 25[/tex]
and
[tex]2x + y = 25[/tex]
We make y the subject in the second equation to get:
[tex]y = 25 - 2x[/tex]
When we substitute into the first equation:
[tex] {x}^{2} + {(25 -2 x)}^{2} = 25[/tex]
Let us expand to get:
[tex] {x}^{2} + 625 - 100x + 4 {x}^{2} = 25[/tex]
We obtain the standard form
[tex]5 {x}^{2} - 100x + 600 = 0[/tex]
Divide through by 5
[tex]{x}^{2} - 20x + 120 = 0[/tex]
The discriminant is
[tex] {( - 20)}^{2} - 4 \times 1 \times 120 = - 80[/tex]
Hence the quadratic equation has no real roots.
This means the line and point has no point of intersection.
