Advertisements
Advertisements
प्रश्न
Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, -3) and B is (1, 4).
Find the coordinates of a point A, where AB is a diameter of a circle with center C (2, -3) and the other end of the diameter is B (1, 4).
उत्तर १
Let the centre of the circle be O.
Since AB is the diameter so, O is the midpoint of AB.
Thus, using the section formula,
`("a" +1)/2 = 2`
⇒ a = 4 - 1
⇒ a = 3
and
`("b" + 4)/2 = -3`
⇒ b = -10
So, the coordinate of point A is (3, -10).
उत्तर २
C (2, -3) is the center of the given circle. Let A(a, b) and B(1, 4) be the two end-points of the given diameter AB. Then, the coordinates of C are
`x = (a+1)/2 , y =( b+4)/2`
It is given that x = 2 and y = -3
⇒ `2= (a+1)/2, 3 = (b+4)/2`
⇒ 4 = a + 1, -6 = b + 4
⇒ a = 4 - 1, b = -6 - 4
⇒ a = 3, b = -10
Therefore, the coordinates of point A are (3, -10).
APPEARS IN
संबंधित प्रश्न
Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.
Find the lengths of the medians of a ∆ABC whose vertices are A(7, –3), B(5,3) and C(3,–1)
Find the coordinates of the centroid of a triangle whose vertices are (–1, 0), (5, –2) and (8, 2)
If the coordinates of the mid points of the sides of a triangle are (1, 1), (2, – 3) and (3, 4) Find its centroid
Three vertices of a parallelogram are (a+b, a-b), (2a+b, 2a-b), (a-b, a+b). Find the fourth vertex.
In what ratio does the point (a, 6) divide the join of (–4, 3) and (2, 8)? Also, find the value of a.
Find the ratio in which the join of (–4, 7) and (3, 0) is divided by the y-axis. Also, find the co-ordinates of the point of intersection.
The point P (5, – 4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B. Given AP is smaller than BP.
Show that A (3, –2) is a point of trisection of the line segment joining the points (2, 1) and (5, −8). Also, find the co-ordinates of the other point of trisection.
A (2, 5), B (–1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that : AP : PB = AQ : QC = 1 : 2.
- Calculate the co-ordinates of P and Q.
- Show that : `PQ = 1/3 BC`.
The line segment joining A (2, 3) and B (6, –5) is intercepted by x-axis at the point K. Write down the ordinate of the point K. Hence, find the ratio in which K divides AB. Also, find the coordinates of the point K.
A(20, 0) and B(10, –20) are two fixed points. Find the co-ordinates of the point P in AB such that : 3PB = AB. Also, find the co-ordinates of some other point Q in AB such that : AB = 6 AQ.
If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:
Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection.
Find the ratio in which the point R ( 1, 5) divides the line segment joining the points S (-2, -1) and T (5, 13).
Using section formula, show that the points A(7, −5), B(9, −3) and C(13, 1) are collinear
Point P(– 4, 6) divides point A(– 6, 10) and B(m, n) in the ratio 2:1, then find the coordinates of point B
If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is ______.
The vertices of a parallelogram in order are A(1, 2), B(4, y), C(x, 6) and D(3, 5). Then (x, y) is ______.
The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 1 : 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.
