If the curves, x^(2) – 6x + y^(2) + 8 = 0 and x^(2) – 8y + y^(2) + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.

C_(1) : x^(2) + y^(2) – 6x + + 8 = 0 C_(1)(3, 0) and r_(1) = 1 C_(2) : x^(2) + y^(2) – 8y + 16 – k = 0 C_(2)(0, 4) and r_(2) = sqrt k Two circles touch each other Therefore C_(1)C_(2) = | r_(1) ± r_(2) | => 5 = | 1 ± sqrt k | Therefore 1 + sqrt k = 5 or sqrt k - 1 = 5 => k = 16 or k = 36 So largest value of k = 36.

If the curves x2 6x y2 8 0 and x2 8y y2 16 k 0 k andgt ... | null (Mathematics)

C₁ : x² + y² – 6x + + 8 = 0

C₁(3, 0) and r₁ = 1

C₂ : x² + y² – 8y + 16 – k = 0

C₂(0, 4) and r₂ =

\sqrt k

Two circles touch each other

\therefore

C₁C₂ = | r₁

\pm

r₂ |

\Rightarrow

5 = | 1

\pm

\sqrt k

\therefore

1 +

\sqrt k

= 5 or

\sqrt k

- 1 = 5

\Rightarrow

k = 16 or k = 36

So largest value of k = 36.

Explanation

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