Application of DerivativeHard
Question
The points on the curve 9y2 = x3 where the normal to the curve makes equal intercepts with coordinates axes is-
Options
A.
B.
C.
D.None of these
Solution
Let the point on the curve 9y2 = x3 is P(x1, y1)
2 × 9 × y ×
= 3x2
Normal of slope = -
so
= ± 1
= 1
-3y1 × 2 = x21 so 9 ×
= x31
so
= - 1
2 × 3y1 = x21 .... (i)
also lies point on the curve 9y2 = x3
9 y21 = x31
9 ×
= x31
x1 = 4
x1 = 4, y1 =
finally point are
or 
2 × 9 × y ×
= 3x2Normal of slope = -
so
= ± 1 = 1-3y1 × 2 = x21 so 9 ×
= x31so
= - 12 × 3y1 = x21 .... (i)
also lies point on the curve 9y2 = x3
9 y21 = x31
9 ×
= x31 x1 = 4
x1 = 4, y1 =
finally point are
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