The centre of a circle is (2x – 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units.
Answers
Answer:
x = 2 or -46/13
Step-by-step explanation:
Hi,
Given diameter of the circle = 20 units
Radius of the circle = d/2 = 20/2 = 10 units
Given center of a circle is (2x - 1, 3x + 1)
Given that circle passes through (-3, -1),
So, distance of (-3, -1) from the center of the circle should be equal to radius
of the circle
Hence, √(2x + 2)² + (3x + 2)² = 10
Squaring on both sides, we get
(2x + 2)² + (3x + 2)² = 100
13x² + 20x - 92 = 0
13x² -26x + 46x -92 = 0
13x(x - 2) + 46(x - 2) = 0
(13x + 46)(x - 2) = 0
Hence, x = 2 or -46/13
Hope, it helps !
Answer:
Given diameter of the circle = 20 units
Radius of the circle = d/2 = 20/2 = 10 units
Given center of a circle is (2x - 1, 3x + 1)
Given that circle passes through (-3, -1),
So, distance of (-3, -1) from the center of the circle should be equal to radius
of the circle
Hence, √(2x + 2)² + (3x + 2)² = 10
Squaring on both sides, we get
(2x + 2)² + (3x + 2)² = 100
13x² + 20x - 92 = 0
13x² -26x + 46x -92 = 0
13x(x - 2) + 46(x - 2) = 0
(13x + 46)(x - 2) = 0
Hence, x = 2 or -46/13
Hope, it helps !
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