# Points on circle

In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are integers. How many points is it?

Result

n =  12

#### Solution:

The equation has the following integer solutions:
x^2 + y^2 = 25
##### x1=-5, y1=0x2=-4, y2=3x3=-4, y3=-3x4=-3, y4=4x5=-3, y5=-4x6=0, y6=5x7=0, y7=-5x8=3, y8=4x9=3, y9=-4x10=4, y10=3x11=4, y11=-3x12=5, y12=0

Number of solutions found: 12

Calculated by our Diofant problems and integer equations.

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### To solve this verbal math problem are needed these knowledge from mathematics:

For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. Do you solve Diofant problems and looking for a calculator of Diofant integer equations? Pythagorean theorem is the base for the right triangle calculator.

## Next similar examples:

1. Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
2. Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
3. Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
4. Sales of products
For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
5. The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
6. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
7. MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
8. Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
9. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
10. R triangle
Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
11. The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r
12. Plumber
Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
13. Segments
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
14. Cuboid walls
Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
15. Cherries
Cherries in the bowl can be divided equally among 19 or 13 or 28 children. How many is the minimum cherries in the bowl?
16. Diofant 2
Is equation ? solvable on the set of integers Z?
17. Seedcake
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?