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
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
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.
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay
The midpoint of the line segment joining A (2a, 4) and B (-2, 3b) is C (1, 2a+1). Find the values of a and b.
Find the ratio which the line segment joining the pints A(3, -3) and B(-2,7) is divided by x -axis Also, find the point of division.
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and } B(0, 2y) of ∆\] AOB .
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0 and B (0, b) are
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
Ordinate of all points on the x-axis is ______.
Abscissa of a point is positive in ______.
The point whose ordinate is 4 and which lies on y-axis is ______.
