00:01
Okay, let's answer this question.
00:03
We need to show that the point satisfies the equation of the unit circle.
00:08
So for a unit circle, the equation of an unit circle is x squared plus y squared equals 1.
00:14
This represents radius.
00:16
The radius of unit circle is 1.
00:18
And so therefore, we can say that x squared plus y squared equals 1.
00:23
Now, we have to substitute this point, show that we can prove that this point lies into the unit circle.
00:31
We have already substituted this x coordinate and here we have to substitute the y colony that is a negative 24 over 25 so we fill negative 24 by 25 in this box and this means we have to square this negative 24 by 25 so this will be negative 24 by 20 square and this equals negative 24 quantity square divided by 25 square and this equals negative 24 222 square is a positive number 576 divided by 25 square is 625 and so here we write 5706 over 625 so then in the next step we add these two fractions that is with this we add 49 over 625 so this equals 5706 plus 49 because the denominator is common 5 -76 plus 49 is 625 and then the denominator is 625 and this exactly equals 1.
01:34
So here we put 1 and this means we are able to see that x squared plus y squared equal to 1 which proves this equation and so we say that the point lies on the unit circle.
01:53
Or in fact we can also say that this is on the circle.
01:57
So if the option is ease, we can choose ease over here.
02:01
The point is on the circle.
02:06
Let's answer this question.
02:08
Here we determine the missing coordinate of the point p.
02:12
We are told that this point p lies on the image circle.
02:16
So therefore we can utilize this equation that is x squared plus y squared and this equals 1.
02:23
So let's determine x from this equation.
02:27
So x will be x squared and then we plug in this y.
02:31
Y coordinate is negative 7 by 25 so this will be 20 squared and this equals 1 i solve for x from this one so here we get x squared plus this one will be 49 over 625 this equals 1 now let's subtract this 49 over 25 from both sides and so we get x squared equals 1 minus 49 over 625 we can rewrite this one as 625 as 6.
03:02
25 over 625 to have a common denominator.
03:07
Now you can subtract these two.
03:09
625 minus 49.
03:11
This equals 576 divided by the common denominator 625.
03:16
So we get the equation x squared equals 576 over 625.
03:23
To solve for x, we take square root on both sides.
03:26
And when you take the square root, this will be square root of 576.
03:32
Divided by square root of 25 and we get two values square root of 576 is when we use the calculator it is 24 so this will be 24 over square root of 625 is 25 and we can put the plus minus because we are taking the square root however we are told that the point is on the coordinate 4 in coordinate 4 the x coordinate is positive so we can take only the positive value for x...