Question

if two curves y=x^2-1 y=ax^2-4x+1 at (1,0) touch each other a=​

Answer 1

Given :

The two curves equations as

y = x² - 1                 .....1

And

y = a x² - 4 x + 1                  .........2

Both the curves touches at point   ( x , y ) = ( 1 , 0 )

To Find :

The value of a

Solution :

As Both the curves touches each other

So, From eq1 and eq 2

x² - 1   =  = a x² - 4 x + 1  

∵  curves touches points ( 1 , 0 ) , so it must satisfy the curve

i.e  (1)² - 1   =  a (1)² - 4 × 1 + 1  

Or,  1 - 1 = a - 4 + 1

Or , 0 = a - 3

∴     a = 3

Hence, The value of a for the curves touches each other is 3  Answer

Answer 2

The value of 'a' is 3

Given:

y = x² - 1 → (equation 1)

y = ax² - 4x + 1 → (equation 2)

Both curves touches at the point (1, 0).

Step-by-step explanation:

Now, on equating the equations of curves, we get,

x² - 1 = ax² - 4x + 1

Since, both curves touch at (1, 0), we get,

1 - 1 = a - 4 + 1

0 = a - 3

∴ a = 3