Eric Nicholas K's answer to LockB's Secondary 3 A Maths Singapore question.
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“Touches” is another expression for “cuts the curve at exactly one point” and this translates to two real and equal roots.
The reason why I took p = 0 as a borderline case is that the equation x2 + y2 = 8p, which becomes x2 + y2 = 0, is technically NOT a curve at all. This represents the equation of a “circle” centred at (0, 0) with radius sqrt (0), so this is technically not a circle at all - it’s just a single point (0, 0) and nothing else. So it’s not really correct to say that the line intersects the curve, when the line actually intersects only a point.
In the other case where p = 10, the equation x2 + y2 = 80 is a circle centred at
(0, 0) with radius sqrt (80). You will learn more on the equation of circles either late in Sec 3 A Maths or early in Sec 4 A Maths.
The reason why I took p = 0 as a borderline case is that the equation x2 + y2 = 8p, which becomes x2 + y2 = 0, is technically NOT a curve at all. This represents the equation of a “circle” centred at (0, 0) with radius sqrt (0), so this is technically not a circle at all - it’s just a single point (0, 0) and nothing else. So it’s not really correct to say that the line intersects the curve, when the line actually intersects only a point.
In the other case where p = 10, the equation x2 + y2 = 80 is a circle centred at
(0, 0) with radius sqrt (80). You will learn more on the equation of circles either late in Sec 3 A Maths or early in Sec 4 A Maths.
Date Posted:
4 years ago
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