the-circles-x-y-4x-2y-3-0-and-x-y-2x-4y-3-0-touches-each-other-Find-the-coordinates-of-the-point-of-contact-

Question Number 216630 by Tawa11 last updated on 12/Feb/25

the circles x² + y² -4x -2y +3 =0 and
x² +y² + 2x +4y -3 =0 touches each other
Find the coordinates of the point of contact

Answered by A5T last updated on 12/Feb/25

(ii) - (i) \Rightarrow 6 x + 6 y = 6 \Rightarrow x + y = 1

\Rightarrow {(1 - y)}^{2} + y^{2} - 4 (1 - y) - 2 y + 3 = 0

\Rightarrow y = 0 \Rightarrow x = 1

\Rightarrow The circles touch each other at (1, 0)

Commented by Tawa11 last updated on 13/Feb/25

Thanks sir, I appreciate .

Answered by mr W last updated on 12/Feb/25

{(x - 2)}^{2} + {(y - 1)}^{2} = {(\sqrt{2})}^{2}

{(x + 1)}^{2} + {(y + 2)}^{2} = {(2 \sqrt{2})}^{2}

t o u c h i n g p o i n t :

(2 + \frac{\sqrt{2}}{3 \sqrt{2}} \times (- 1 - 2), 1 + \frac{\sqrt{2}}{3 \sqrt{2}} \times (- 2 - 1))

\Rightarrow (1, 0)

Commented by mr W last updated on 13/Feb/25

Commented by mr W last updated on 13/Feb/25

x_{c} = x_{1} + \frac{r_{1}}{r_{1} + r_{2}} (x_{2} - x_{1})

y_{c} = y_{1} + \frac{r_{1}}{r_{1} + r_{2}} (y_{2} - y_{1})

Commented by Tawa11 last updated on 13/Feb/25

Thanks sir .

I appreciate .

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