Advertisements
Advertisements
प्रश्न
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
Advertisements
उत्तर
Given, the points A(4,3) and B(x,5) lie on a circle with center o(2,3) . Then OA = OB
Also `(OA)^2 = (OB)^2`
`⇒(4-2)^2 + (3-3)^2 = (x-2) ^2 +(5-3)^2`
`⇒(2)^2+(0)^2=(x-2)^2 +(2)^2`
`⇒ 4=(x-2)^2 +4`
`⇒(x-2)^2 =0`
⇒ x -2 = 0
⇒ x =2
Therefore, x= 2
APPEARS IN
संबंधित प्रश्न
If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(4, 5) B(7, 6), C (4, 3), D(1, 2)
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
If the points p (x , y) is point equidistant from the points A (5,1)and B ( -1,5) , Prove that 3x=2y
Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
If (a,b) is the mid-point of the line segment joining the points A (10, - 6) , B (k,4) and a - 2b = 18 , find the value of k and the distance AB.
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
In which quadrant does the point (-4, -3) lie?
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
Point (0, –7) lies ______.
Point (–10, 0) lies ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
