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what is the condition that the line y=mx+c be tangent to a parabola x square =4ay is c=-am square

what is the condition that the line y=mx+c be tangent to a parabola x square =4ay is c=-am square

Grade:12

1 Answers

Nehal Wani
21 Points
11 years ago

y=mx+c........(i)

x2=4ay..........(ii)

Putting the value of y from (i) to (ii)

x2=4a(mx+c)

The line Touches The parabola If Discriminant=0

x2-4amx-c=0

16a2m2=-4c

c=-4a2m2

There fore the equation of tangent is:

y=mx-4a2m2

 

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