the centre of the circle is 2 alpha -1, 3 alpha plus one and it passes through the point - 3 - 1 is a diameter of the circle is of length 20 units find the value of Alpha
Answers
Given : centre of the circle is 2 alpha -1, 3 alpha plus one and it passes through the point - 3 - 1 , Diameter = 20 units
To find : the value of Alpha α
Solution:
center of circle = 2α - 1 , 3α + 1
Diameter = 20 units
=> radius = 20/2 = 10 units
Equation of Circle
(x - h)² + (y - k)² = r²
h . k is center of circle & r = radius
=> (x - 2α + 1)² + (y - 3α - 1)² = 10²
Now Circle passes through -3 , - 1
putting x= - 3 & y = - 1
=> (-3 - 2α + 1)² + (-1 - 3α - 1)² = 10²
=> (-2 - 2α )² + (-2 - 3α)² = 100
=> 4 + 4α² + 8α + 4 + 9α² + 12α = 100
=> 13α² + 20α - 92 = 0
=> 13α² - 26α + 46α - 92 = 0
=> 13α(α - 2) + 46(α - 2) = 0
=> (13α + 46)(α - 2) = 0
α = 2 , α = -46/13
value of Alpha α = 2 or -46/13
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