Does the point (3,6) lie inside the circle x^2 + y^2 = 40?

Question

and why? I know the answer is no, i just don't understand why that is. Ten points !!

Answer 1

(x,y)=(3,6), so filling in the equation give us 9+36 which is larger than 40, so it is not in the circle.

Answer 2

All points that lie inside the circle satisfy this inequality:
x^2 + y^2 ≤ 40

Since x=3 and y=6, plug it in and see if it still holds:
3^2 + 6^2 ≤ 40
9 + 36 ≤ 40
45 ≤ 40

Of course, 45 ≤ 40 is false, so it is NOT inside the circle.

Answer 3

so you know that a coordinate is given in (x,y) right?

so think of it this way:

(x,y) = (3,6)

therefore:
x = 3
y = 6

then just plug 3 in for x and 6 in for y.

x^2 + y^2 = 40

(3)^2 + (6)^2

9 + 36 = 45

since 45 does not = 40, then you know it doesn't lie in the circle.

Answer 4

in any equation, x and y r points which lie on the curve or on the line(in case equation is o a line)
here u ve x as 3
and y as 6
to check if this point lies on the circle or inside or outside the circle, we can put these values in the equation nd find.... as follows

3^2+6^2
= 9+36
= 45
this value is greater than 40 so, the given point lies outside the circle..... if it wud ve been less than 40, it says that point is inside the circle... and when it is equal to 40, it saya that point lies on the circle

Answer 5

x^2 +y^2 = 40 relate a radius of circle.

If you have asked that if point 3,6 (x,y) lie within said circle answer is 'no' ( when both 'origin' of point 3,6 (x,y) and 'center of circle' are same!)

Regards.

Answer 6

To understand why, rewrite the equation of your circle in the most general form, (x-x_c)^2+(y-y_c)^2=r^2, where (x_c, y_c) is the center of the circle and r is the radius. Knowing this explains why (3,6) is outside x^2+y^2=40.

Answer 7

What is the radius of the circle?
What is the centre of the circle?
(These are two things you can answer from the equation).

Then calculate the distance from the centre of the circle to the point (3, 6). Is this distance bigger than he radius? if yes, the point is outside the circle.

Answer 8

r1 ² = 40
r1= √40
r2 ² = 3² + 6² = 45
r2 = √45
r2 > r1 so point lies outside circle.