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Sagot :
The line is passing through the circle then it intersects the circle at the points (8, -1) and (-1, 8). Option A is correct.
What is a circle?
It is a special kind of ellipse whose eccentricity is zero and foci are coincident with each other. It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Given
x² + y² = 65 is a equation of circle.
y + x = 7 equation of line.
Let line is passing through the circle then it will intersect the circle at the point. Then
[tex]\rm y = -x + 7[/tex]
Put this equation in the equation of the circle.
[tex]\begin{aligned} x^{2} + (-x + 7)^2 &= 65 \\\\x^{2} +x^{2} + 49 -14x &= 65\\\\2x^{2} - 14x -16 &= 0\\\\x^{2} - 7 x -8 &= 0\\\\(x - 8)(x + 1) &= 0\\\\x &= 8, - 1\end{aligned}[/tex]
For x = 8, y will be
[tex]\rm y = - 8 + 7\\y = -1[/tex]
For x = -1, y will be
[tex]\rm y = -(-1)+ 7\\y = 8[/tex]
Thus, the points are (8, -1) and (-1, 8).
More about the circle link is given below.
https://brainly.com/question/11833983
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