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What is the best way of differentiating intersection of two curves and touching of curves

What is the best way of differentiating intersection of two curves and touching of curves

Grade:12th pass

1 Answers

Vikas TU
14149 Points
3 years ago
 In this illustration we will utilize the bends y=2x2 , and y=x2+1. This is an exceptionally clear case, yet exhibits the strategy for finding the crossing point of two bends well. 
Step 1 - since the LHS of both these conditions is the same (y=...) we can liken the two conditions: 
2x2=x2+1 
This is a genuinely simple condition to illuminate: 
Lets make one side equivalent to zero: 
- x2 +1=0 
Lets move everything crosswise over to the opposite side to dispose of the less signs. 
x2 - 1 =0 
This is the distinction of two squares, so can be factorized: 
(x+1)(x-1)=0 
So the x-directions of the crossing point focuses are +1 and - 1. 
Step 2 - Now we have to discover the y-facilitates. We do this by connecting the x-qualities to the first conditions. We can utilize it is possible that one, in light of the fact that the lines meet (so they ought to give us a similar outcome!) 
At the point when x= +1, 
y=2x2 
y=2(1)2 =2 
At the point when x= - 1 
y=2(- 1)2 = 2 
So the purposes of crossing point have facilitates (- 1,2) and (1,2) .

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