Given normal to ellipse is
`2x-(8)/(3)lamday=-3`
or `y=((3)/(4lambda))x+((9)/(8lambda))`
Here, `m=(3)/(4lambda)=(9)/(8lambda)`
Now, condition for line y=mx+c to be normed to ellipse is
`C=+-((a^(2)-b^(2))m)/(sqrt(a^(2)+b^(2)m^(2)))`
`rArr(9)/(8lambda)=+-(3(3)/(4lambda))/(sqrt(1+4(9)/(16lambda^(2))))`
`rArr 4lambda^(2)+9=16lambda^(2)`
`rArr4lambda^(2)=3`
`rArr=+-(sqrt(3))/(2)`
Thus, normals are `2x+-(4)/(sqrt(3))y=-3`
