Advertisements
Advertisements
प्रश्न
The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).
विकल्प
True
False
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
Find the distance of the following points from the origin:
(ii) B(-5,5)
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
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.
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
Find distance CD where C(– 3a, a), D(a, – 2a)
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
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 point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
