Finding the vertex, axis, focus, directrix, and latus rectum of the parabola $\sqrt{x/a}+\sqrt{y/b}=1$

Find the vertex, axis, focus, directrix, and length of latus rectum of the parabola $$\displaystyle \sqrt{\frac{x}{a}}+\sqrt{\frac{y}{b}}=1$$

Try: Curve $$\sqrt{\frac{x}{a}}+\sqrt{\frac{y}{b}}=1$$ represents a parabola.

While drawing the diagram, I am getting that the parabola touches $$x$$ axis at $$A(a,0)$$ and touches $$y$$ axis at $$(0,b)$$

Also, the tangents at points $$A$$ and $$B$$ intersect each other at $$(0,0)$$ at an angle of $$90^\circ$$.

I do not know how can I solve this problem. Could someone help me to solve it? Thanks.

A nice property of the parabola states that: the perpendicular from the focus to any tangent intersects it, and the tangent through the vertex, at the same point. Hence, if the tangent at vertex $$V$$ intersect the axes at $$A'=(\alpha,0)$$ and $$B'=(0,\beta)$$, then focus $$F$$ has coordinates $$(\alpha,\beta)$$.
The axis $$FV$$ is perpendicular to $$A'B'$$, hence its slope is $$\alpha/\beta$$. But the tangent at $$A$$ forms equal angles with the axis and $$FA$$, hence the slope of line $$FA$$ is $$-\alpha/\beta$$. The same goes for line $$FB$$, hence we have the equations: $${\beta-b\over\alpha}={\beta\over\alpha-a}=-{\alpha\over\beta},$$ which can be solved to find: $$\alpha={ab^2\over a^2+b^2},\quad \beta={a^2b\over a^2+b^2}.$$ The directrix is the parallel to $$A'B'$$ passing through the origin. The given equation $$\displaystyle \sqrt{\frac{x}{a}}+\sqrt{\frac{y}{b}}=1$$ can be simplified as $$\displaystyle \sqrt{\frac{x}{a}} = 1 - \sqrt{\frac{y}{b}}$$ Squarring both sides, $$\displaystyle \frac{x}{a}= 1 - 2\sqrt{\frac{y}{b}} + \frac{y}{b}$$ $$\displaystyle \frac{x}{a}-1+ \frac{y}{b}=- 2\sqrt{\frac{y}{b}}$$ Squarring again, $$\displaystyle \left(\frac{x}{a}-1+ \frac{y}{b}\right)^2=4\frac{y}{b}$$ $$\displaystyle \left(X\right)^2=4Y$$ Where $$X=\frac{x}{a}-1+ \frac{y}{b}$$ and $$Y=\frac{y}{b}$$ Now compare with the standard form, apply the formulae and find the required properties.