Application of DerivativeHard
Question
If the tangent to the curve 2y3 = ax2 + x3 at a point (a, a) cuts off intercepts p and q on the coordinates axes, where p2 + q2 = 61, then a equals-
Options
A.30
B.-30
C.0
D.± 30
Solution
Curve 2y3 = ax2 + x3 at point (a, a)
diff. w.r.t. x
= 6y2 ×
= 2ax + 3x2
tangent equation
y - a =
(x - a)
6y - 6a = 5x - 5a
5x - 6y - a = 0
= 1
p =
, q = 
p2 + q2 =
= 61
a2
= 61
a = ± 5 × 6
diff. w.r.t. x
= 6y2 ×
= 2ax + 3x2tangent equation
y - a =
(x - a)6y - 6a = 5x - 5a
5x - 6y - a = 0
= 1p =
, q = p2 + q2 =
= 61a2
= 61a = ± 5 × 6
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