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Consider the two functions f(x) =x^2+2bx+1 and g(x)=2a(x+b), where the variable x and the constants a and b are real numbers. Each such pair of the constants a and b may be considered as a point (a,b) in an ab - plane.Let S be the set of such points (a,b) for which the graphs of y=f(x) and y=g(x) do not intersect (in the xy- plane). The area of S =?

 
Consider the two functions f(x) =x^2+2bx+1 and g(x)=2a(x+b), where the variable x and the constants a and b  are real numbers. Each such pair of the constants a and b may be considered as a point (a,b) in an ab - plane.Let S be the set of such points (a,b) for which the graphs of y=f(x) and y=g(x) do not intersect (in the xy- plane). The area of S =? 
 

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
Giventwo functions f(x) =x^2+2bx+1 and g(x)=2a(x+b), where the variable x and the constants a and b are real numbers. Each such pair of the constants a and b may be considered as a point (a,b) in an ab - plane.
Let S be the set of such points (a,b) for which the graphs of y=f(x) and y=g(x) do not intersect (in the xy- plane).
For them not to intersectx^2+2bx+1 =2a(x+b) on simplifying we get
x^2+2(b-a)x+1-2ab=0.................(1)
For them not to intersect the discriminant of eqn(1) should be less than zero
By Simplifying the discriminant we get a2+b2<1
Which represents a circle with an area of\pi
So the area of S=\pi

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