Advertisements
Advertisements
प्रश्न
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
उत्तर
Let the coordinates of the point on y-axis be (0, y).
From the given information, we have:
`sqrt((0 + 8)^2 + (y - 4)^2)` = 10
(0 + 8)2 + (y - 4)2 = 100
64 + y2 + 16 - 8y = 100
y2 - 8y - 20 = 0
y2 - 10y + 2y - 20 = 0
y(y - 10) + 2(y - 10) = 0
(y - 10)(y + 2) = 0
y = 10, - 2
Thus, the required co-ordinates of the points on y-axis are (0, 10) and (0, -2).
APPEARS IN
संबंधित प्रश्न
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
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
A(1,-3) and B(4,-6)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
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.
Find the distance of the following point from the origin :
(0 , 11)
Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3`sqrt 5` units.
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
The distance between points P(–1, 1) and Q(5, –7) is ______
Show that P(– 2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle
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:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
|
Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
