CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Auxiliary Circle of Ellipse

The number of...

Question

The number of lattice points (lattice points are points with both coordinate integers) on the circle with centre (199, 0) and radius 199 is___

Open in App

Solution

Equation of circle is $(x - 199)^{2} + y^{2} = 199^{2}$
$x = 199 + 199 c o s θ, y = 199 s i n θ s i n θ = 1 \Rightarrow (199, 199) s i n θ = 0 \Rightarrow (398, 0), (0, 0)$
$s i n θ = - 1 \Rightarrow (199, - 199)$ are the only points.

Suggest Corrections

thumbs-up

0

Similar questions

Q. Find maximum number of points having integer coordinates (both

x, y

integer) which can lie on a circle with centre at

(\sqrt{2}, \sqrt{3})

Q. We define a lattice point as a point whose coordinates are integers, zero admitted. Then the number of lattice points on the boundary and inside the region bounded by the x-axis, y-axis, the line

x = 4

y = 4

Q. A circle K centered at

(0, 0)

is given. Prove that for every vector

(a_{1}, a_{2})

there is a positive integer n such that the circle K translated by the vector

n (a_{1}, a_{2})

contains a lattice point (i.e., a point both of whose coordinates are integers)

Q. A mineral having formula

A B_{2}

crystallises in the cubic close-packed lattice, with the

A

atoms occupying the lattice points. Hence coordination number of

A

B

Q. The maximum number of points with rational coordinates on a circle with radius

2

& whose centre is

(\sqrt{3}, 0)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Parametric Representation-Ellipse

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Auxiliary Circle of Ellipse

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon