Advertisements
Advertisements
प्रश्न
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
Advertisements
उत्तर
Radius of the circle = 30 units.
The point O is (0, 0).
Let a intersect the x-axis and b intersect the y-axis.
∴ The point A is (a, 0) and B is (0, b)
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
OA = `sqrt(("a" - 0)^2 + (0 - 0)^2`
30 = `sqrt("a"^2)`
Squaring on both sides
302 = a2
∴ a = 30
The point A is (30, 0)
OB = `sqrt((0 - 0)^2 + ("b" - 0)^2`
= `sqrt(0^2 + "b"^2)`
30 = `sqrt("b"^2)`
Squaring on both sides
302 = b2
∴ b = 30
The point B is (0, 30)
Distance AB = `sqrt((30 - 0)^2 + (0 - 30)^2`
= `sqrt(30^2 + 30^2)`
= `sqrt(900 + 900)`
= `sqrt(1800)`
= `sqrt(2 xx 900)`
= `30sqrt(2)`
∴ Distance between the two points = `30sqrt(2)`
APPEARS IN
संबंधित प्रश्न
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = 6, y = - 2
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
-9, -1
Co-ordinate of point P on a number line is - 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.
Determine whether the given set of points are collinear or not
(a, −2), (a, 3), (a, 0)
Show that the following points taken in order to form the vertices of a parallelogram
A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)
Verify that the following points taken in order to form the vertices of a rhombus
A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)
Verify that the following points taken in order to form the vertices of a rhombus
A(1, 1), B(2, 1), C(2, 2) and D(1, 2)
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, −4) and (5, −6)
If the points A(2, 0), B(– 6, 0), C(3, a – 3) lie on the x-axis then the value of a is _____
