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The equation of the parabola to which the line m^2(y-10)-mx-1=0 is a tangent for any real value of m

The equation of the parabola to which the line m^2(y-10)-mx-1=0 is a tangent for any real value of m

Grade:12

2 Answers

Arun
25757 Points
3 years ago
Dear student
 
Question is incomplete. Please check and repost the question. You can also attach an image. Na dif possible please post options too. as they are required.
 
Aditya Gupta
2081 Points
3 years ago
hello mounika. fromwe know that am^2) for all values of m.2am, at (= 4ay  is a tagnent to the parabola x^2y = mx - am^2 ….... (1)
m^2(y-10)-mx-1=0 can be written as (y-10)= x/m+1/m^2
or Y= nx – ( – 1)n^2 .........(2), where n= 1/m (and hence n can also be any real since m can vary over the reals) and Y= y – 10
on comparing (2) and (1) we have a= – 1
so, the corresponding parabola would be x^2 = 4aY
substituting values
x^2 = 4*( – 1)(y – 10)
or x^2 + 4(y – 10) = 0
kindly approve :))

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