For what value of lambda does the line y = x | vedclass

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(C) The equation of the ellipse is $9x^2 + 16y^2 = 144$.Dividing by $144$,we get $\frac{x^2}{16} + \frac{y^2}{9} = 1$.Comparing this with $\frac{x^2}{

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$\pm 5$

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(C) The equation of the ellipse is $9x^2 + 16y^2 = 144$.Dividing by $144$,we get $\frac{x^2}{16} + \frac{y^2}{9} = 1$.Comparing this with $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,we have $a^2 = 16$ and $b^2 = 9$.The line equation is $y = x + \lambda$,which is of the form $y = mx + c$,where $m = 1$ and $c = \lambda$.The condition for the line $y = mx + c$ to touch the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is $c^2 = a^2m^2 + b^2$.Substituting the values,we get $\lambda^2 = 16(1)^2 + 9$.$\lambda^2 = 16 + 9 = 25$.Therefore,$\lambda = \pm 5$.

For what value of $\lambda$ does the line $y = x + \lambda$ touch the ellipse $9x^2 + 16y^2 = 144$?

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