Solution:-
Given:
Major axis on the x-axis and passes through the points (4, 3) and (6, 2).
Since the major axis is on the 
-axis, the equation of the ellipse will be the form
Where ‘ 
is the semi-major axis.]
The ellipse passes through points 
and 
So by putting the values 
and 
in equation (1), we get, 
Putting, 
and 
in equation (1), we get,
From equation (2)
Substituting the value of 
in equation (3) we get,
![\begin{array}{l} 36 / a^{2}+4 / b^{2}=1 \\ 36\left(1 / a^{2}\right)+4 / b^{2}=1 \\ 36\left[1 / 16\left(1-9 / b^{2}\right)\right]+4 / b^{2}=1 \\ 36 / 16\left(1-9 / b^{2}\right)+4 / b^{2}=1 \\ 9 / 4\left(1-9 / b^{2}\right)+4 / b^{2}=1 \\ 9 / 4-81 / 4 b^{2}+4 / b^{2}=1 \\ -81 / 4 b^{2}+4 / b^{2}=1-9 / 4 \\ (-81+16) / 4 b^{2}=(4-9) / 4 \\ -65 / 4 b^{2}=-5 / 4 \\ -5 / 4\left(13 / b^{2}\right)=-5 / 4 \\ 13 / b^{2}=1 \\ 1 / b^{2}=1 / 13 \\ b^{2}=13 \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d21b7f208ffa32bd1f67f85827d9810f_l3.png "Rendered by QuickLaTeX.com")
Now substitute the value of 
in equation (4) we get,
Equation of ellipse is 
By substituting the values of 
and in above equation we get, 