Porisma

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Find a normal and distinguish its second curve intersection

For x=4t/(1−t2)x=4t/(1-t^2), y=1/(1−t2)y=1/(1-t^2), show the normal at P(8/3,4/3)P(8/3,4/3) is 3y=−15x+443y=-15x+44. It meets the curve again at Q; find t at Q.

[2006//PJC/II/3]

CJC · Lecture · Example 11

Use both coordinates to choose the sign of the parameter at P.

Read the worked solution