$\text{ The eccentric angle of a point on the ellipse }\frac{x^2}{4}+\frac{y^2}{3}=1\text{ at a distance of }5/4\text{ units from the focus on the positive x- axis is}$

$\begin{array}{l}\text{ Any point on the ellipse is }(2\cos \theta ,\sqrt{3}\sin \theta )\text{ . }\\ \text{ The focus on the positive }x\text{ -axis is }(1,0)\text{ . }\end{array}$

$\begin{array}{r}(2\cos \theta -1{)}^2+3{\sin }^2\theta =\frac{25}{16}\\ \text{or }\cos \theta =\frac{3}{4}\end{array}$