Difference between revisions of "1957 AHSME Problems/Problem 34"

Revision as of 07:13, 26 July 2024

Problem

The points that satisfy the system $x + y = 1,\, x^2 + y^2 < 25$ , constitute the following set:

$\textbf{(A)}\ \text{only two points} \qquad \\ \textbf{(B)}\ \text{an arc of a circle}\qquad \\ \textbf{(C)}\ \text{a straight line segment not including the end-points}\qquad\\ \textbf{(D)}\ \text{a straight line segment including the end-points}\qquad\\ \textbf{(E)}\ \text{a single point}$

Solution

$[asy] import geometry; // Axes draw((0,-8)--(0,8),arrow=Arrows); label("$y$",(0,9)); draw((-8,0)--(8,0),arrow=Arrows); label("$x$",(9,0)); // Circle and Line draw(circle((0,0),5),red+dashed); draw(line((0,1),(1,0)),blue); [/asy]$

$\fbox{\textbf{(C)} a straight line segment not including the end-points}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 33	Followed by Problem 35
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Difference between revisions of "1957 AHSME Problems/Problem 34"

Revision as of 07:13, 26 July 2024

Problem

Solution

See Also

@@ Line 9: / Line 9: @@
 == Solution ==
+<asy>
+import geometry;
+// Axes
+draw((0,-8)--(0,8),arrow=Arrows);
+label("$y$",(0,9));
+draw((-8,0)--(8,0),arrow=Arrows);
+label("$x$",(9,0));
+// Circle and Line
+draw(circle((0,0),5),red+dashed);
+draw(line((0,1),(1,0)),blue);
+</asy>
 <math>\fbox{\textbf{(C)} a straight line segment not including the end-points}</math>.