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.
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
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
Determine the ratio in which the point P (m, 6) divides the join of A(-4, 3) and B(2, 8). Also, find the value of m.
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.
Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).
Find the area of triangle with vertices ( a, b+c) , (b, c+a) and (c, a+b).
If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
