Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.