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Hyperbola Transformation Question?

sooo i need a bit of help with this question, i understand the answer because i did the graph sketches but i don't really know how to solve it w/o them?

'State clearly the geometrical transformation involves in transforming the curve y=2x² into the curve y²=2x'

I started off with reflecting in y=x which gave 2y²=x, but then i'm not sure how to get that to y²=2x ? can someone explain ?? thanks

Reply 1

atsruser

Original post by ithinkitslily

You have

2y^2=x \Rightarrow y^2=\frac{x}{2}

so you can now either:

a) stretch/shrink the y-axis or
b) stretch/shrink the x-axis

The stretch factors in these cases will differ; it's easier to do the x-axis.