Question

Heya All, Need an accurate answer for this mellifluous question.

(x-4) ^2013. (x+8)^ 2014. (x+1)/x^2016(x-2)³. (x+3)^5 (x-6)(x+9)^2012 <= 0
Represent this in no. line by wavy curve method and find the no. of positive integrals.

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Answer 1

Answer:

Hint: We compare the given equation of circle with general equation of circle x2+y2+2gx+2fy+c=0x2+y2+2gx+2fy+c=0 and find the radius of the circle as g2+f2−c−−−−−−−−−√g2+f2−c. We use the wavy curve method for what values of λλ the radius is less than 5.

Complete step-by-step solution:

We know that the general equation of circle in two variables is given by the equation,

x2+y2+2gx+2fy+c=0x2+y2+2gx+2fy+c=0

We know the radius rr of the above circle is given by

r=g2+f2−c−−−−−−−−−√r=g2+f2−c

We are given the equation from the question with parameter λλ as,

x2+y2+λx+(1−λ)y+5=0x2+y2+λx+(1−λ)y+5=0

We compare the coefficients of xx, coefficients of yy and the constant term of the equation with equation of general circle to have

g=−λ2,f=−(1−λ)2,c=5g=−λ2,f=−(1−λ)2,c=5

So the radius of the circle is given by;

r=(−λ2)2+(−(1−λ)2