Question

What is one of the solutions to the following system of equations? y2 x2 = 65 y x = 7 (8, −1) (1, 6) (6, 1) (9, −2).

Answer 1

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

$\rm y = -x + 7$

Put this equation in the equation of the circle.

$\begin{aligned} x^{2} + (-x + 7)^2 &= 65 \\\\x^{2} +x^{2} + 49 -14x &= 65\\\\2x^{2} - 14x -16 &= 0\\\\x^{2} - 7 x -8 &= 0\\\\(x - 8)(x + 1) &= 0\\\\x &= 8, - 1\end{aligned}$

For x = 8, y will be

$\rm y = - 8 + 7\\y = -1$

For x = -1, y will be

$\rm y = -(-1)+ 7\\y = 8$

Thus, the points are (8, -1) and (-1, 8).

More about the circle link is given below.

brainly.com/question/11833983