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The line 3x + 4y = 24 meets the x-axis and y-axis at points A and B, respectively, while the line 4x + 3y = 24 intersects at points C and D. The four points A, B, C, and D are located on which type of curve?
- a circle
- a parabola
- an ellipse
- a hyperbola
Correct answer: a circle
Solution
3x+4y=24 cuts the axes at A(8,0), B(0,6); 4x+3y=24 cuts them at C(6,0), D(0,8). The x-intercepts multiply to 8*6=48 and the y-intercepts to 6*8=48 (equal), the condition for the four points to lie on a circle. So the curve is a circle, option index 0, not the stored ellipse (index 2).
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