If x + y + k = 0 is a tangent to the circle x 2 + y 2 - 2x - 4y + 3 = 0 then k = Options: A . &nbsp ± 20 B . &nbsp –1, – 5 C . &nbsp ± 2 D . &nbsp 4

Answer: Option B : B Radius = Distance from the centre C(1, 2) to x + y + k = 0 ⇒ √ 1 + 4 − 3 = | 1 + 2 + k | √ 2 ⇒ | k + 3 | = 2 ⇒ k + 3 = ± 2 ⇒ k = -1, - 5

If x + y + k = 0 is a tangent to the circle x2+y2 - 2x

Discussion Forum : Circles

Question -

If x + y + k = 0 is a tangent to the circle $x^{2} + y^{2}$ - 2x - 4y + 3 = 0 then k =

Options:

A .

\pm

B . –1, – 5

C .

\pm

D . 4

Answer: Option B
:
B
Radius = Distance from the centre C(1, 2) to x + y + k = 0

\Rightarrow

\sqrt{1 + 4 - 3}

\frac{| 1 + 2 + k |}{\sqrt{2}}

\Rightarrow

| k + 3 |

= 2

\Rightarrow

k + 3 =

\pm

\Rightarrow

k = -1, - 5

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