`A B` is a variable line sliding between the coordinate axes in such a way that `A` lies on the x-axis and `B` lies on the y-axis. If `P` is a variable point on `A B` such that `P A=b ,P b=a` , and `A B=a+b ,` find the equation of the locus of `Pdot`

Explanation

Let p(h,k) be the point
In `hPMB,
sintheta=(MB)/(PB) and costheta=b/a`

In`/_\PNA
sintheta=k/h,costheta=(AN)/b`

∴ From both the /_\ s,

`sintheta=k/b & costheta=h/a`

∵`sin^2theta+cos^2theta=1`

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