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The greatest distance of the point P(10, 7) from the circle x2 + y2 – 4x – 2y – 20 = 0 is
- a)5
- b)15
- c)10
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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The greatest distance of the point P(10, 7) from the circle x2+ y2&nda...
The equation of the circle is x^2 + y^2 = r^2, where r is the radius of the circle. We need to find the value of r first.
The circle passes through the origin (0,0), since x^2 + y^2 = 0^2 when x = 0 and y = 0. Therefore, the distance from the center of the circle to the origin is equal to the radius.
The center of the circle is at (0,0), so the distance from the center to the point P(10,7) is:
d = sqrt((10-0)^2 + (7-0)^2) = sqrt(149)
Therefore, the radius of the circle is r = sqrt(149).
The greatest distance from the point P(10,7) to the circle is the distance from the point to the edge of the circle along a line that passes through the center of the circle. This is equal to the difference between the distance from the center to the point and the radius of the circle.
The distance from the center of the circle to the point P(10,7) is d = sqrt((10-0)^2 + (7-0)^2) = sqrt(149).
Therefore, the greatest distance of the point P(10,7) from the circle is:
d - r = sqrt(149) - sqrt(149) = 0.
Therefore, the greatest distance is 0, which means that the point P(10,7) is on the circle.
The circle passes through the origin (0,0), since x^2 + y^2 = 0^2 when x = 0 and y = 0. Therefore, the distance from the center of the circle to the origin is equal to the radius.
The center of the circle is at (0,0), so the distance from the center to the point P(10,7) is:
d = sqrt((10-0)^2 + (7-0)^2) = sqrt(149)
Therefore, the radius of the circle is r = sqrt(149).
The greatest distance from the point P(10,7) to the circle is the distance from the point to the edge of the circle along a line that passes through the center of the circle. This is equal to the difference between the distance from the center to the point and the radius of the circle.
The distance from the center of the circle to the point P(10,7) is d = sqrt((10-0)^2 + (7-0)^2) = sqrt(149).
Therefore, the greatest distance of the point P(10,7) from the circle is:
d - r = sqrt(149) - sqrt(149) = 0.
Therefore, the greatest distance is 0, which means that the point P(10,7) is on the circle.
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The greatest distance of the point P(10, 7) from the circle x2+ y2–4x –2y –20 = 0 isa)5b)15c)10d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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