Advertisements
Advertisements
प्रश्न
If the points p (x , y) is point equidistant from the points A (5,1)and B ( -1,5) , Prove that 3x=2y
उत्तर
As per the question, we have
AP = BP
`⇒ sqrt((x -5)^2 +(y-1)^2) = sqrt((x+1)^2 +(y-5)^2)`
`⇒(x-5)^2 +(y-1)^2 = (x+1)^2 +(y-5)^2` (Squaring both sides)
`⇒x^2 - 10x +25 + y^2 -2y +1 = x^2 +2x +1+y^2 -10y+25`
⇒ - 10x -2y =2x-10y
⇒ 8y = 12x
⇒3x=2y
Hence, 3x=2y.
APPEARS IN
संबंधित प्रश्न
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
Find the co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2
The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
Find the values of x for which the distance between the point P(2, −3), and Q (x, 5) is 10.
If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
Any point on the line y = x is of the form ______.
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
