Question #70926
how to find the double point of the curve y^2 = (x-2)^2 (x-1) ?
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#339914 on Dec 2023
#339914 on Dec 2023
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it's my pleasure...
Thank you for correcting us.
i think it will be node because when we shift the curve from (0,0) to point (2,0), then the new origin will be (2,0) . and equation of tangent at origin is given by equating to zero the lowest degree terms . so we get two distinct and real tangent and this result shows that it must be node at point (2,0) .
The possible double points are (2,0) and (4/3 ,0) . but out of these only (2,0) satisfy the equation of curve . thus (2,0) is the only double point of given curve. and at (2,0) not cusp its will be node.