Question

Find the equation of the normal to the parabola y 2 +4x = 0 at the point where the line y = x+c touches it.

Answer 1

Answer: x+y+3=0

Step-by-step explanation:

To find equation of normal to parabola y^2+4x=0 or y^2= -4x where the line touches y = x + c touches it...

Here, we can see that a= -1 from parabola and slope of tangent (m1)= 1 from line

Then, slope of normal (m2)= -1

Now, from formulae in terms of m

Equation of normal,

y=mx-2am-am-am^3

Now, putting all the values of a and m we get, m=-1 and a=-1

y=-x-2-1

y=-x-3

x+y+3=0

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