Advertisements
Advertisements
प्रश्न
The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.
Advertisements
उत्तर
Distance between the points A (2x - 1, 3x + 1) and B (- 3, - 1) = Radius of circle
AB = 10 (Since, diameter = 20 units, given)
AB2 = 100
(-3 - 2x + 1)2 + (-1 - 3x - 1)2 = 100
(-2 - 2x)2 + (-2 - 3x)2 = 100
4 + 4x2 + 8x + 4 + 9x2 + 12x = 100
13x2 + 20x - 92 = 0
x = `(-20 ± sqrt(400 + 4784))/(26)`
x = `(-20 ± 72)/(26)`
x = 2, - `(46)/(13)`.
APPEARS IN
संबंधित प्रश्न
Find the distance between the points:
P(a + b, a - b) and Q(a - b, a + b)
Find the distance between the following pairs of point in the coordinate plane :
(13 , 7) and (4 , -5)
Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.
From the given number line, find d(A, B):
Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.
If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
The distance of the point P(–6, 8) from the origin is ______.
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
The distance between the points (0, 5) and (–3, 1) is ______.
