Maths-
General
Easy
Question
Assertion: Through (
+ 1) there can not the more than one normal to the parabola y2 = 4x if + 
< 2.
Reason: The point ( + 1) lie out side the parabola for all 
1.
- If both (A) and (R) are true, and (R) is the correct explanation of (A).
- If both (A) and (R) are true but (R) is not the correct explanation of (A).
- If (A) is true but (R) is false.
- If (A) is false but (R) is true.
The correct answer is: If both (A) and (R) are true but (R) is not the correct explanation of (A).
Any normal to the parabola
y2 = 4x is
y + t x = 2t + t3
If this passes through (+ 1)
Thus we get + 1 + t = 2 t + t3
t3 + t (2 – ) – – 1 = 0 (f(t) say)
If < 2 then f '(t) = 3t2 + (2 – ) > 0
f(t) = 0 will have only one real root
A is true.
The Reason R is also true since ( + 1)2 > 4 is true for all 1. The assertion A is true but does not follow true R.
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