Q. 104.2( 309 Votes )
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Answer :
To Find: Relation between x and y
Given: (x, y) is equidistant from (3, 6) and (-3, 4)
From the figure it can be seen that Point (x, y) is equidistant from (3, 6) and (- 3, 4)
This means that the distance of (x, y) from (3, 6) will be equal to distance of (x, y) from (- 3, 4)
We know by distance formula that, distance between two points A(x1, y1), B(x2, y2) is given by
Therefore,
√[(x- 3)2 + (y - 6)2] = √[(x + 3)2 + (y- 4)2]
Squaring both sides, we get
(x – 3)2 + (y – 6)2 = (x + 3)2 + (y – 4)2
x2 + 9 – 6x + y2 + 36 – 12y = x2 + 9 + 6x + y2 + 16 – 8y
36 – 16 = 6x + 6x + 12y – 8y
20 = 12x + 4y
3x + y = 5
3x + y – 5 = 0 is the relation between x and y
Rate this question :
Section Formula30 mins
Measuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE Questions29 mins
Smart Revision | Become a Master in Coordinate Geometry54 mins
Distance Formula and Section Formula44 mins
NCERT | Quiz on Section Formula43 mins
Imp. Qs. on Distance Formula68 mins
Champ Quiz | Distance Formula30 mins
Set of Questions on Section Formula54 mins
Smart Revision | Coordinate Geometry46 mins
Using distance formula, examine whether the following sets of points are collinear?
(- 1, 2), (5, 0), (2, 1)
KC Sinha - MathematicsUsing distance formula, examine whether the following sets of points are collinear?
(0, 0), (9, 6), (3, 2)
KC Sinha - MathematicsProve that the distance between the points (a + rcosθ, b + rsinθ) and (a, b) is independent of θ.
KC Sinha - Mathematics