$\"\"$

The equation of ellipse is $\"\"$ .

The particle travels in tangent path of the ellipse at $\"\"$ .

Find the slope of the equation.

$\"\"$

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Find the slope of the tangent line at the point $\"\"$ .

Slope of the tangent line is the first derivative of the function at point $\"\"$ .

$\"\"$

Find the tangent line equation.

Slope-intercept form of line equation is $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$ .

Find the point at which the particle crosses the $\"\"$ -axis.

It crosses $\"\"$ -axis then $\"\"$ .

$\"\"$

Therefore, the particle crosses the $\"\"$ -axis at $\"\"$ .

$\"\"$

The particle crosses the $\"\"$ -axis at $\"\"$ .