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snow_lady [41]
3 years ago
10

The straight line y=2x-2 meets the circle x^2+y^2=8 at the points A and B. Find the length of AB, giving your answer correct to

one decimal place.​
Mathematics
1 answer:
Alex73 [517]3 years ago
8 0

Answer:

(12/5)√5

Step-by-step explanation:

y = 2x - 2

x² + y² = 8

x² + (2x - 2)² = 8

x² + 4x² - 8x + 4 = 8

5x² - 8x - 4 = 0

(5x + 2)(x - 2) = 0

x = -2/5

x = 2

y = 4 - 2

y = 2

(2,2)

y = 2(-2/5) - 2

y = -4/5 - 2

y = -14/5

(-2/5,-14/5)

√((2 + 2/5)² + (2 + 14/5)²)

√((12/5)²+ (24/5)²)

√(144/25 + 576/25)

(1/5)√(144+576)

(1/5)√720

(1/5)√(16*45)

(4/5)√45

(12/5)√5

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