Advertisements
Advertisements
प्रश्न
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
विकल्प
(0, 2)
(2, 0)
(3, 0)
(0, 3)
Advertisements
उत्तर
Let A(−1, 0) and B(5, 0) be the given points. Suppose the required point on the x-axis be P(x, 0).
It is given that P(x, 0) is equidistant from A(−1, 0) and B(5, 0).
∴ PA = PB
⇒ PA2 = PB2 \[\Rightarrow \left[ x - \left( - 1 \right) \right]^2 + \left( 0 - 0 \right)^2 = \left( x - 5 \right)^2 + \left( 0 - 0 \right)^2\] (Using distance formula)
\[\Rightarrow \left( x + 1 \right)^2 = \left( x - 5 \right)^2 \]
\[ \Rightarrow x^2 + 2x + 1 = x^2 - 10x + 25\]
\[ \Rightarrow 12x = 24\]
\[ \Rightarrow x = 2\]
Thus, the required point is (2, 0).
APPEARS IN
संबंधित प्रश्न
Find the distance between the following pair of points:
(a, 0) and (0, b)
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
Points (−4, 0) and (7, 0) lie
The perpendicular distance of the point P (4, 3) from x-axis is
If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.
ABCD is a parallelogram with vertices \[A ( x_1 , y_1 ), B \left( x_2 , y_2 \right), C ( x_3 , y_3 )\] . Find the coordinates of the fourth vertex D in terms of \[x_1 , x_2 , x_3 , y_1 , y_2 \text{ and } y_3\]
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(−2, 6) and C(3, 1) is 10 square units.
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.
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
Find the distance between the points \[\left( - \frac{8}{5}, 2 \right)\] and \[\left( \frac{2}{5}, 2 \right)\] .
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
f 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
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
