What are you asking? You will NOT get a quadratic equation by solving those equations- theyarequadratic. And, contrary to your title, there are no linear equations here.

If you do mean "solve following equation" which variable do you want to solve for?

To solve I for X, subtract (Y- Y1)^2/b^2 from both sides to get (X-X1)/a^2= 1- (Y-Y1)^2/b^2. Multiply both sides by a^2 to get (X-X1)^2= a^2(1- (Y-Y1)^2/b^2). Take the square root of both sides to get X- X1= +/- a sqrt(1- (Y-Y1)^2/b^2). Finally add X1 to both sides to get X= X1 +/- a sqrt{1- (Y-Y1)^2/b^2). That is neither a "linear" nor a "quadratic" equation.

To solve it for Y, Do the same thing but keep Y on the left side rather than X.

To solve II for X or Y, pretty much the same thing but easier- you don't have an "a" or "b" to worry about.