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CGP EDU Academic Team
Published on: August 13, 2026
A normal is drawn at a point P (x, y) of a curve. It meets the x-axis and the y-axis in point A and B, respectively, such that 
+ 
= 1, where O is the origin, find the equation of such a curve passing through (5, 4) -
Text Solution
Verified by ExpertsThe correct answer is:
B
The equation of the normal at (x, y) is :
(X – x) + (Y – y) 
= 0
⇒ 
+ 
= 1
⇒ OA = x + y 
, OB = 
Also, 
= 1
⇒ 1 + 
= x + y 
⇒ (y – 1) 
+ (x – 1) = 0
Integrating, we get
(y – 1) 2 + (x – 1) 2 = c
Since the curve passes through (5, 4), c = 25.
Hence, the curve is (x – 1) 2 + (y – 1) 2 = 25
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