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Verdich [7]
2 years ago
12

Consider equation of circle x2-2x+y2-4y-4=0,if line 2x-y+a=0 is its diameter then find value of a

Mathematics
1 answer:
g100num [7]2 years ago
4 0

Answer:

Step-by-step explanation:

x² - 2x + y² - 4y - 4 = 0

x² - 2x + y² - 4y = 4

complete the squares

(x² - 2x + x₀) + (y² - 4y + y₀) = 4

the unknown number will be the square of half of the x¹ coefficient

(x² - 2x + 1) + (y² - 4y + 4) = 4 + 1 + 4

(x - 1)² + (y - 2)² = 9

This tells us that the circle is centered on (1, 2)

Which is also a point on the diameter

2x - y + a = 0

a = y - 2x

a = 2 - 2(1)

a = 0

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DI = 38

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\frac{DI}{76} = \frac{1}{2}  ( cross- multiply )

2DI = 76 ( divide both sides by 2 )

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