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प्रश्न
The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.
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उत्तर
Distance between the points A (2x - 1, 3x + 1) and B (- 3, - 1) = Radius of circle
AB = 10 (Since, diameter = 20 units, given)
AB2 = 100
(-3 - 2x + 1)2 + (-1 - 3x - 1)2 = 100
(-2 - 2x)2 + (-2 - 3x)2 = 100
4 + 4x2 + 8x + 4 + 9x2 + 12x = 100
13x2 + 20x - 92 = 0
x = `(-20 ± sqrt(400 + 4784))/(26)`
x = `(-20 ± 72)/(26)`
x = 2, - `(46)/(13)`.
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Case Study -2
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It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
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Read the following passage:
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Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
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- Show that for Shagun, school is farther compared to Alia's house and library.
OR
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