Advertisements
Advertisements
Question
The point (x, y) is equidistant from the points (3, 4) and (−5, 6). Find a relation between x and y
Advertisements
Solution
Let the point O be (x, y), A be (3, 4) and B be (−5, 6).
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Given, OA = OB
`sqrt((x - 3)^2 + (y - 4)^2) = sqrt((x + 5)^2 + (y - 6)^2`
Squaring on both sides
(x – 3)2 + (y – 4)2 = (x + 5)2 + (y – 6)2
x2 – 6x + 9 + y2 – 8y + 16 = x2 + 10x + 25 + y2 – 12y + 36
x2 + y2 – 6x – 8y + 25 = x2 + y2 + 10x – 12y + 61
6x – 10x – 8y + 12y = 61 – 25
⇒ – 16x + 4y = 36 ........(÷ 4)
⇒ – 4x + y = 9
∴ The relation between x and y is y = 4x + 9
APPEARS IN
RELATED QUESTIONS
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, R) + d(R, Q) = d(P, Q)
Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.
3, 6
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
x + 3, x - 3
Determine whether the given set of points are collinear or not
(7, −2), (5, 1), (3, 4)
Determine whether the given set of points are collinear or not
(a, −2), (a, 3), (a, 0)
Show that the following points taken in order to form the vertices of a parallelogram
A(−7, −3), B(5, 10), C(15, 8) and D(3, −5)
Verify that the following points taken in order to form the vertices of a rhombus
A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
Find the distance with the help of the number line given below.
d(B, E)
Find the distance with the help of the number line given below.
d(P, J)
