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If ` 4x-3y+k=0` touches the ellipse ` 5x^(2)+9y^(2)=45` , then k is equal to

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If ` 4x-3y+k=0` touches the ellipse ` 5x^(2)+9y^(2)=45` , then k is equal to
A. ` pm 3 sqrt(21)`
B. `3 sqrt(21)`
C. `-3 sqrt(21)`
D. `2 sqrt(21)`
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1 Answer

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Correct Answer - A
If line ` 4x-3y+k=0` touches the
ellipse `(x^(2))/(9)+(y^(2))/(5)=1 ` , then
`(k)/(3)=sqrt(9 xx((4)/(3))^(2)+5)=pm sqrt(21)`
`implies k = pm 3sqrt(21)`
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