Advertisements
Advertisements
Question
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
Advertisements
Solution
Let P(x, 0) be the point on the x-axis.
Then as per the question we have
AP = 10
`\implies sqrt((x - 11)^2 + (0 + 8)^2` = 10
`\implies` (x – 11)2 + 82 = 100 ...(Squaring both sides)
`\implies` ( x – 11)2 = 100 – 64
`\implies` ( x – 11)2 = 36
`\implies` x – 11 = ±6
`\implies` x - 11 = 6 or x - 11 = -6
`\implies` x = 6 + 11 or x = -6 + 11
`\implies` x = 17 or x = 5
Hence, the points on the x-axis are (17, 0) and (5, 0).
RELATED QUESTIONS
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
Find the values of x for which the distance between the point P(2, −3), and Q (x, 5) is 10.
Find the distance between the points \[\left( - \frac{8}{5}, 2 \right)\] and \[\left( \frac{2}{5}, 2 \right)\] .
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
The distance of the point (4, 7) from the y-axis is
Write the equations of the x-axis and y-axis.
Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).
Ordinate of all points on the x-axis is ______.
Find the coordinates of the point which lies on x and y axes both.
Seg AB is parallel to X-axis and coordinates of the point A are (1, 3), then the coordinates of the point B can be ______.
