Let O(0,0) and A(0,1) be two fixed points. Then, the locus of a...

$⇒ PO + PA = 3$

$⇒$Locus of $P$ is ellipse with foci at $O$ & $A$ and major

axis \left(2b\right) = 3$</p><p>Distance between foci$= 2be = 1 ⇒ e = \dfrac{1}{3}$</p><p>$⇒$Minor axis$2a = 2b\sqrt{1 - {e}^{2}} = 3 . \dfrac{2\sqrt{2}}{3} = 2\sqrt{2}$</p><p>$⇒$Equation of Locus of$P$is :</p><p>$\dfrac{{x}^{2}}{8} + \dfrac{{\left(y - \dfrac{1}{2}\right)}^{2}}{9} = \dfrac{1}{4}$</p><p>By simplifying the above equation, we get</p><p>$9{x}^{2} + 8{y}^{2} - 8y = 16