Q. 244.1( 8 Votes )
The points on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes are
A. 
B. 
C. 
D. 
Answer :
It is given that the equation of the curve is 9y2 = x3
Differentiating w.r.t. x, we get,
The slope of the normal to the given curve at point (x1,y1) is
Then, the equation of the normal to the curve at (x1,y1)is
⇒ y – y1 =
⇒ 
⇒ 
⇒ 
⇒ 
Now, it is given that the normal makes equal intercepts with the axes.
Thus, we get,
⇒ 
⇒ 
⇒ 
…………………….(1)
Since, the point (x1,y1)lies on the curve 
…………(2)
From (1) and (2), we get
Now putting the value of x1 in (2), we get
Therefore, the required points are 
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