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CGP EDU Academic Team
Published on: August 14, 2026
If the tangent to the curve 2y 3 = ax 2 + x 3 at the point (a, a) cuts off intercepts α and β on the coordinate axes, where α 2 + β 2 = 61 then the value of | a | is -
Text Solution
Verified by ExpertsThe correct answer is:
C
The slope of the tangent is
= 
and the value of this slope at (a, a) is 5/6.
Therefore, the equation
y – a = 
(x – a) ⇒ 
+ 
= 1,
represents the tangent. Thus the x-intercept α is –a/5, and the y-intercept β is a/6. From α 2 + β 2 = 61, we now get 
= 61
⇒ a 2 = 25 × 36 ⇒ a = ± 30.
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