Question
If the line x + y = k is a normal to the parabola y2 = 4x,then the value of k will be-
- 2
- 1
- 3
- 4
Hint:
equation of normal of a parabola : y= mx -2am-am3
The correct answer is: 3
k= 3
Given parabola: y2=4x
Equation of normal of y2=4ax
: y= mx -2am-am3. Here, a = 1
Given normal : y= x- k
On comparing, we get
m =1 and -k= -2-1 = -3
k=3
the equation of tangent and normal in terms of the slope of the parabola are used to find the equations for any given slope.
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