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Question
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
Options
True
False
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Solution
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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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 y axis equidistant from B and C is ______.
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, – 9) and has diameter `10sqrt(2)` units.
The distance between the points (0, 5) and (–3, 1) is ______.
