Advertisements
Advertisements
प्रश्न
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
उत्तर
It is given that the coordinates of point A are such that its ordinate is twice its abscissa.
So, let the coordinates of point A be (x, 2x).
We have:
`sqrt((x - 4)^2 + (2x - 3)^2) = sqrt(10)`
(x - 4)2 + (2x - 3)2 = 10
x2 + 16 - 8x + 4x2 + 9 - 12x = 10
5x2 - 20x + 25 = 10
5x2 - 20x = 10 - 25
5x2 - 20x = - 15
5x2 - 20x + 15 = 0
x2 - 4x + 3 = 0
x2 - x - 3x + 3 = 0
x(x - 1) -3(x - 1) = 0
(x - 1)(x - 3) = 0
x = 1, 3
Thus, the co-ordinates of the point A are (1, 2) and (3, 6).
APPEARS IN
संबंधित प्रश्न
If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Find the distance of the following points from the origin:
(i) A(5,- 12)
Find all possible values of y for which distance between the points is 10 units.
Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , `sqrt 5`) and R (`-2 sqrt 2` , -1). Also find its radius.
Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.
Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.
From the given number line, find d(A, B):
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
