Question

If the coordinates of a variable point `P` are `(acostheta,bsintheta),` where `theta` is a variable quantity, then find the locus of `Pdot`

Answer 1

Let `P -=(x,y)`. According to the question,
`x=acostheta`(1)
`y=bsintheta` (2)
Sqaureing and adding (1) and (2), we get
`(x^2)/(a^2)+(y^2)/(b^2)=cos^2theta+sin^2theta`
or `(x^2)/(a^2)+(y^2)/(b^2)=1`