Radius squared is 1 squared plus –8 squared, which is 65. For D: (–5) squared plus 6 squared is 61. Since 61 is less than 65, D is inside. For E: 0 squared plus 9 squared is 81. E is outside.
(i) Given the points A (1, – 8), B (– 4, 7) and C (–7, – 4), show that they lie on a circle K whose center is the origin O (0, 0). What is the radius of circle K? (ii) Given the points D (–5, 6) and E (0, 9), check whether D and E lie within the circle, on the circle or outside the circle K.
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(i) By calculating the distance from the origin O (0, 0) to points A, B and C using the formula (x squared plus y squared), we find all equal 65. Thus, they lie on circle K with a radius of the square root of 65. (ii) For point D (–5, 6), the sum is 61, which is less than 65, placing it inside the circle. For point E (0, 9), the sum is 81, placing it outside the circle.
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Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/