Advertisements
Advertisements
प्रश्न
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
पर्याय
1
2
0
-1
उत्तर
We have three collinear points A(a,0) ; B ( 0 , b ) ; C (1 , 1 ) .
In general if `A(x_1,y_1) ;B(x_2 ,y_2) ;C(x_3 ,y_3)` are collinear then,
`x_1 (y_2 -y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) = 0`
So,
a(b- 1 )+ 0 (1 - 0) + 1(0 - b) = 0
So,
ab = a + b
Divide both the sides by (ab) ,
`1/a + 1/b = 1`
APPEARS IN
संबंधित प्रश्न
On which axis do the following points lie?
R(−4,0)
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
If A(3, y) is equidistant from points P(8, −3) and Q(7, 6), find the value of y and find the distance AQ.
If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
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.
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
If the distance between the points (4, p) and (1, 0) is 5, then p =
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0 and B (0, b) are
