## Question

For what value of λ dose the line *y = x *+ λ touches the ellipse 9*x*^{2} + 16*y*^{2} = 144.

### Solution

Equation of ellipse is 9*x*^{2} + 16*y*^{2} = 144

Comparing this with

Then we get *a*^{2} = 16 and *b*^{2} = 9 and comparing the line *y = x *+ λ with *y = mx + c*

*m* = 1 and *c* = λ

If the line *y = x *+ λ touches the ellipse

9*x*^{2} + 16*y*^{2} = 144, then

*c*^{2} = *a*^{2}*m*^{2} + *b*^{2}

.

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