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
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the distance between the points
A(-6,-4) and B(9,-12)
Find the distance of the following points from the origin:
(i) A(5,- 12)
Find all possible values of x for which the distance between the points
A(x,-1) and B(5,3) is 5 units.
Find all possible values of y for which distance between the points is 10 units.
Find the distances between the following point.
A(a, 0), B(0, a)
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.
Find the distance of the following points from origin.
(a+b, a-b)
Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
The distance between the points (0, 5) and (–3, 1) is ______.
Read the following passage:
|
Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
|
Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
-
- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
