Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Find the distance between the points
(i) A(9,3) and B(15,11)
Find the distance between the points
A(1,-3) and B(4,-6)
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the abscissa of point Q.
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
The distance between points P(–1, 1) and Q(5, –7) is ______
Find distance between point A(– 3, 4) and origin O
Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
The distance of the point (5, 0) from the origin is ______.
