The area of a square garden is 1 / 81 km^2. How long is each side?
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Answer:
Compare the given equation of the circle (x - 1)² + (y -2)² = 2²
with standard form of circle: (x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle
and r is the radius of the circle.
Thus, The center of the circle is: (1, 2)
Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,
Substitute the value of y from equation of line in the equation of circle.
(x - 1)² + (2x + 2 - 2)² = 2²
⇒ (x - 1)² + (2x)² = 2²
⇒ x² + 1 - 2x + 4x² = 4
⇒ 5x² - 2x - 3 = 0
Applying Middle term splitting method
5x² - 5x + 3x - 3 = 0
⇒ 5x(x - 1) + 3(x - 1) = 0
⇒ (5x + 3)(x - 1) = 0
⇒ x = and x = 1
Thus, we get coordinates: and (1, 4)