Find the number of points of intersection of the system $\left\{ \begin{array} { c }
x ^ { 2 } + y ^ { 2 } = 16 \
x - y = 1
\end{array} \right.$
A) one
B) three
C) two
D) four

Question

Find the number of points of intersection of the system $\left\{ \begin{array} { c } 
x ^ { 2 } + y ^ { 2 } = 16 \
x - y = 1
\end{array} \right.$
A) one
B) three
C) two
D) four

Quizplus · Accepted Answer

The system consists of a circle with radius 4 (from $x^2 + y^2 = 16$) and a straight line (from $x - y = 1$). The line intersects the circle at two distinct points, as it is not tangent to the circle nor does it miss the circle entirely.

Find the Number of Points of Intersection of the System {x2+y2=16x−y=1\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 16 \\x - y = 1\end{array} \right.{x2+y2=16x−y=1​

Find the Number of Points of Intersection of the System $\left\{ \begin{array} { c } x ^ { 2 } + y ^ { 2 } = 16 \\x - y = 1\end{array} \right.$