Advertisements
Advertisements
प्रश्न
Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
उत्तर
The given points are A(-1, y) , B(5,7) and O(2, -3y).
Here, AO and BO are the radii of the circle. So
AO = BO ⇒ AO2 = BO2
`⇒ (2+1)^2+(-3-y)^2 = (2-5)^2 +(-3y-7)^2`
`⇒ 9+(4y)^2 = (-3)^2 +(3y+7)^2`
`⇒9+16y^2=9+9y^2 +49+42y`
`⇒ 7y^2 -42y^2 -49=0`
`⇒y^2 -6y-7=0`
`⇒y^2-7y+y-7=0`
`⇒y(y-7)+1(y-7)=0`
`⇒(y-7)(y+1)=0`
`⇒y=-1or y =7`
Hence , y=7 or y=-1
APPEARS IN
संबंधित प्रश्न
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
The measure of the angle between the coordinate axes is
The perpendicular distance of the P (4,3) from y-axis is
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
In which quadrant does the point (-4, -3) lie?
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
Point (–10, 0) lies ______.
The points whose abscissa and ordinate have different signs will lie in ______.
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?
Find the coordinates of the point which lies on x and y axes both.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
Co-ordinates of origin are ______.
