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प्रश्न
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
पर्याय
True
False
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उत्तर
This statement is False.
Explanation:
If the distance between the centre and any point is equal to the radius, then we say that point lie on the circle.
Now, distance between P(–2, 4) and centre (3, 5)
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((3 + 2)^2 + (5 - 4)^2`
= `sqrt(5^2 + 1^2)`
= `sqrt(25 + 1)`
= `sqrt(26)`
Which is not equal to the radius of the circle.
Hence, the point P(–2, 4) does not lies on the circle.
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संबंधित प्रश्न
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
The value of 'a' for which of the following points A(a, 3), B (2, 1) and C(5, a) a collinear. Hence find the equation of the line.
Find the distance between the following pair of points:
(a+b, b+c) and (a-b, c-b)
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
Find the distance between the points
(ii) A(7,-4)and B(-5,1)
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
A line segment of length 10 units has one end at A (-4 , 3). If the ordinate of te othyer end B is 9 , find the abscissa of this end.
From the given number line, find d(A, B):
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
The points A (3, 0), B (a, -2) and C (4, -1) are the vertices of triangle ABC right angled at vertex A. Find the value of a.
Find distance between point Q(3, – 7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = – 7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
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