Expert Answer to "Find the coordinates of the points of intersection..."

snowlovelydayM

Answered question

2021-08-10

Find the coordinates of the points of intersection of each of the following pairs of circles.
a.

x^{2} + y^{2} - 3 x + 5 y - 4 = 0

and

x^{2} + y^{2} - x + 4 y - 7 = 0

Viktor Wiley

Skilled2021-08-11Added 84 answers

Step 1
Since you have asked multiple questions in single request so we will be answering only first question.
Given:
a) a.

x^{2} + y^{2} - 3 x + 5 y - 4 = 0 \to 1

x^{2} + y^{2} - x + 4 y - 7 = 0 \to 1

Step 2

- 2 x + y + 3 = 0

\Rightarrow y = - 3 + 2 x \to 3

Substitute value of y in 1,

x^{2} + {(- 3 + 2 x)}^{2} - 3 x + 5 (- 3 + 2 x) - 4 = 0

Step 3

x^{2} + (9 - 12 x + 4 x^{2}) - 3 x + 5 (2 x - 3) - 4 = 0

x^{2} + 9 - 12 x + 4 x^{2} - 3 x + 10 x - 15 - 4 = 0

\Rightarrow 5 x^{2} - 5 x - 10 = 0

\Rightarrow x^{2} - x - 2 = 0

\Rightarrow x^{2} - 2 x + x - 2 = 0

\Rightarrow x (x - 2) + 1 (x - 2) = 0

\Rightarrow (x - 2) (x + 1) = 0

\Rightarrow x = - 1, x = 2

Step 4
but these values of x in 3,

y = - 3 + 2 (- 1) = - 5

y = - 3 + 2 (2) = 1

\Rightarrow

points of intersection are

(- 1, - 5)

and

(2, 1)

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