How to find the image of the curve with equation y=1/x^2?

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1 Answer
Feb 3, 2018

y=-9/(x^2+4x+4)-1

Explanation:

All points on the curve y=1/x^2 will have coordinates of the form:

(k,1/k^2)

[(3,0),(0,-1)][(k),(1/k^2)]=[(3k),(-1/k^2)]+[(-2),(-1)]=[(3k-2),(-1/k^2-1)]

i.e. x'=3k-2 , y'=-1/k^2-1

Eliminating k:

i.e.

k=(x'+2)/3

y'=-1/((x+2)/3)^2-1=-1/(((x^2+4x+4))/9)-1=-9/(x^2+4x+4)-1

Equation is:

y=-9/(x^2+4x+4)-1