Advertisements
Advertisements
प्रश्न
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
उत्तर
P lies on x-axis and Q lies on y-axis
Let abscissa P be x then ordinate of Q is x - 1
∴ P(x , 0) , Q (0 , x - 1)
Given PQ = 5 units
`sqrt (("x" - 0)^2 + (0 - x + 1)^2) = 5`
squaring both sides
x2 + x2 + 1 - 2x = 25
2x2 - 2x - 24 = 0
x2 - x - 12 = 0
x2 - 4x + 3x - 12 = 0
(x - 4)(x + 3) = 0
x = + 4 or - 3
Coordinates of P are (4,0) or (-3,0)
Coordinates of Q are (0,3) or (0,-4)
APPEARS IN
संबंधित प्रश्न
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Find the distance of the following point from the origin :
(5 , 12)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Find the distance between the points (a, b) and (−a, −b).
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
