Advertisements
Advertisements
प्रश्न
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Advertisements
उत्तर
As per the question, we have
AP = BP
`⇒sqrt((2+2)^2 +(2+k)^2) = sqrt(( 2+2k)^2 +(2+3)^2)`
`⇒sqrt((4)^2 +(2-k)^2) = sqrt((2+2k)^2 + (5)^2)`
⇒ 16+ 4 +k2 - 4k = 4+ 4k2 + 8k +25 (Squaring both sides)
`⇒k^2 + 4k +3=0`
⇒ (k+1) (k+3) =0
⇒ k =-3, -1
Now for k = -1
`AP= sqrt ((2+2)^2 +(2-k)^2)`
`= sqrt((4)^2 +(2+1)^2)`
`= sqrt(16+9) = 5` units
For k = -3
`AP= sqrt(( 2+2)^2 +(2-k)^2)`
`= sqrt((4)^2+(2+3)^2)`
`=sqrt(16+25) = sqrt(41)` units
Hence, k= -1,-3; AP= 5 units for k=-1 and AP=`sqrt(41)` units for k=-3.
APPEARS IN
संबंधित प्रश्न
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
In what ratio does the line x - y - 2 = 0 divide the line segment joining the points A (3, 1) and B (8, 9)?
Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
The ordinate of any point on x-axis is
The perpendicular distance of the point P (4, 3) from x-axis is
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
In which quadrant does the point (-4, -3) lie?
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x-axis?
