Question

If x + y + k = 0 is a tangent to the circle
x2 + y2 – 2x – 4y + 3 = 0 then k​

Answer 1

Given info : x + y + k = 0 is a tangent to the circle x² + y² - 2x - 4y + 3 = 0.

To find : The value of k.

solution : here equation of circle is.. x² + y² - 2x - 4y + 3 = 0

centre of circle = (1, 2) and radius of circle = √(1² + 2² - 3) = √2

if x + y + k = 0 is a tangent of circle x² + y² - 2x - 4y + 3 = 0.

so radius of circle = distance of tangent from the centre

⇒√2 = |1 + 2 + k|/√(1² + 1²)

⇒√2 × √2 = |3 + k|

⇒2 = |3 + k|

⇒k + 3 = ±2

⇒k = -5 or -1

Therefore the values of k are -5 and -1.

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Answer 2

Given Info :-

• x + y + k = 0 is a tangent to the circle x² + y² - 2x - 4y + 3 = 0.

To Find :-

• The value of k.

Solution :-

Equation of circle is ➙ x² + y² - 2x - 4y + 3 = 0

• centre of circle = (1, 2)
• radius of circle = √(1² + 2² - 3) = √2

Radius of circle = distance of tangent from the centre

➙√2 = |1 + 2 + k|/√(1² + 1²)

➙√2 × √2 = |3 + k|

➙2 = |3 + k|

➙k + 3 = ±2

➙k = -5 and -1

Therefore , the values of k are -5 and -1.

★Hope it helps u★