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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
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Find the distance between the points
(i) A(9,3) and B(15,11)
Find all possible values of y for which distance between the points is 10 units.
Find value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
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.
A(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the origin and the point:
(-5, -12)
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Point P (2, -7) is the centre of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of AB.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
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.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
The point on x axis equidistant from I and E is ______.
Find the distance between the points O(0, 0) and P(3, 4).
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
