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प्रश्न
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
विकल्प
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:
(a, b), (−a, −b)
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Find the distance between the points
A(-6,-4) and B(9,-12)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.
Distance of point (−3, 4) from the origin is ______.
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance of the following point from the origin :
(8 , 15)
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
PQR is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.
Find the distance between the origin and the point:
(-5, -12)
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
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.
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
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`
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:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
