Advertisements
Advertisements
Question
Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
Advertisements
Solution
We have P(x, y), Q(-3, 0) and R(3, 0)
`PQ = sqrt((x + 3)^2 + (y - 0)^2)`
`=> 4 = sqrt(x^2 + 9 + 6x + y^2)`
Squaring both sides
`=> (4)^2 = (sqrt(x^2 + 9 + 6x + y^2))`
`=> 16 = x^2 + 9 + 6x + y^2`
`=> x^2 + y^2 = 16 - 9 - 6x`
`=> x^2 + y^2 = 7 - 6x` ......(1)
`PR = (sqrt((x - 3)^2 + (y - 0)^2)`
`=> 4 = sqrt(x^2 + 9 - 6x + y^2)`
Squaring both sides
`(4)^2 = (sqrt(x^2 + 9 - 6x + y^2))`
`=> 16 = x^2 + 9 - 6x + y^2`
`=> x^2 + y^2 = 16 - 9 + 6x`
`=> x^2 + y^2 = 7 + 6x` .....(2)
Equating (1) and (2)
7 - 6x = 7 + 6x
⇒ 7 - 7 = 6x + 6x
⇒ 0 = 12x
⇒ x = 0
Substituting the value of x = 0 in (2)
`x^2 + y^2 = 7 + 6x`
`0 + y^2 = 7 + 6 xx 0`
`y^2 = 7`
`y = +- sqrt7`
APPEARS IN
RELATED QUESTIONS
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Find the distances between the following point.
A(a, 0), B(0, a)
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.
Prove that the following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
