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secondary 3 | A Maths
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secondary 3 chevron_right A Maths chevron_right Singapore

pls explain too :)

Date Posted: 4 years ago
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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
1st
“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.