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प्रश्न
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
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उत्तर
The given points A(4, 3) and B(x, 5) lie on the circle with center O(2, 3). Then, OA = OB
`⇒ sqrt((x-2)^2 +(5-3)^2) = sqrt((4-2)^2 +(3-3)^2)`
`⇒ (x-2)^2 +2^2 =2^2+0^2`
`⇒ (x-2)^2 = (2^2 -2^2)`
`⇒ (x-2)^2=0`
⇒ x - 2 = 0
⇒ x = 2
Hence, the value of x = 2
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संबंधित प्रश्न
The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Find the points of trisection of the line segment joining the points:
5, −6 and (−7, 5),
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
The abscissa and ordinate of the origin are
The perpendicular distance of the P (4,3) from y-axis is
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
Write the X-coordinate and Y-coordinate of point P(–5, 4).
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
