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Question
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 ______.
Options
Touch each other
Cut at right angle
Cut at an angle `pi/3`
Cut at an angle `pi/4`
Solution
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 cut at right angle.
Explanation:
From first equation of the curve
We have 3x2 – 3y2 – 6xy `"dy"/"dx"` = 0
⇒ `"dy"/"dx" = (x^2 - y^2)/(2xy)` = (m1) say and second equation of the curve gives
`6xy + 3x^2 "dy"/"dx" - 3y^2 "dy"/"dx"` = 0
⇒ `"dy"/"dx" = (-2y)/(x^2 - y^2)` = (m2) say
Since m1 . m2 = –1.
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