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प्रश्न
Find the distance of the following points from origin.
(a cos θ, a sin θ).
उत्तर
Let p(a cos θ, a sin θ) and O(0 , 0)
Then | OP | = `sqrt((a cos theta - 0)^2 + (a sin theta - 0)^2)`
= `sqrt(a^2 cos^2 theta + a^2 sin^2 theta)`
= `sqrt(a^2 (sin^2 theta + cos^2 theta)`
= `asqrt(1)`
= a units.
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संबंधित प्रश्न
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 following pair of points:
(a+b, b+c) and (a-b, c-b)
Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).
The distance of the point (α, β) from the origin 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 ______.
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.
