The values of `lamda` for which the line y=x+`lamda` touches the ellipse `9x^(2)+16y^(2)=144` , are

Options

A. `+-5`
B. `+-4`
C. `+-12`
D. `+-3`

Answer

A

Explanation

the equation of the line is
`y=x+ lamda`
compairing it with y= mx + c, we get
`m=1 and c= lamda`
the equation of the ellipse is
`9x^(2)+16y^(2)=144 or ,(x^(2))/(16)+(y^(2))/(9)=1`
comparing this with `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` we get `a^(2) = 16 and b^(2) =9`
if the touches the ellipse , then
`c^(2)=a^(2)m^(2)+b^(2)implies lamda ^(2) = 16 +9implieslamda =+- 5.`