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A B is a variable line sliding betwee...

`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`

Text Solution

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Let `P(h,k)` be a variable point on AB such that `angleOAB=theta`.
Here, `theta` is a variable from triangles ALP and PMB.we have
`sintheta=(k)/(b)` (1)
`cos theta= (h)/(a) ` (2)
Here, `theta` is a variable so, we have to elimiante `theta`. Squareing (1) and (2) and adding, we get
`(k^2)/(b^2)+(h^2)/(a^2)=1`
`(x^2)/(a^2)+(y^2)/(b^2)=1`
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