Q. 234.0( 6 Votes )
The normal to the curve x2 = 4y passing (1,2) is
A. x + y = 3
B. x – y = 3
C. x + y = 1
D. x – y = 1
Answer :
It is given that the equation of curve is x2 = 4y
Differentiating w.r.t. x, we get,
The slope of the normal to the given curve at point (h,k) is
Then, the equation of the normal to the curve at (h,k) is
⇒ y – k =
Now, it is given that the normal passes through the point (1,2)
Thus, we get,
⇒ 2 – k =
⇒ k = 
………………(1)
Since (h,k) lies on the curve x2 = 4y, we have h2 = 4k
⇒ k = 
Now putting the value of of k in (1), we get
⇒ h3 = 8
⇒ h = 2
Therefore, the equation of the normal is given as:
⇒ y – 1 = 
⇒ y - 1 = - (x - 2)
⇒ x + y = 3
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