Get the solution to "Write the equation of a line passing through..."

Alyce Wilkinson

Answered question

2021-08-17

Write the equation of a line passing through the centers of the two circles

{(x - 3)}^{2} + {(y + 2)}^{2} = 16

and

{(x - 6)}^{2} + {(y + 1)}^{2} = 25

Answer & Explanation

au4gsf

Skilled2021-08-18Added 95 answers

Step 1
Comparing with standard equation of a circle ic
${(x - h)}^{2} + {(y - k)}^{2} = s^{2}$ wher $(h, k) :$ center of circle
From equation (1), centre: $(h_{1}, k_{1}) = (3, - 2)$
Froma equation (2), centre: $(h_{2}, k_{2}) = (6, - 1)$
Step 2
Since equation of a line bassing through two paints
$(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by,
$y - y_{1} = (\frac{y_{2} - y_{1}}{x_{2} - x_{1}}) (x - x_{1})$
$∴$ equation of siqusid line,
$y - k_{1} = (\frac{k_{2} - k_{1}}{h_{2} - h_{1}}) (x - h_{1})$
$y + 2 = (\frac{- 1 + 2}{3}) (x - 3)$
$y + 2 = \frac{1}{3} (x - 3)$
$y = \frac{1^{x - 1 - 2}}{3}$
$y = \frac{1^{x - 3}}{3}$ "

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