What is the radius of a circle whose equation is x2 y2 8x − 6y 21 0

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Algebra

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What is the radius of a circle whose equation is x2+y2−10x+6y+18=0? 2 units 4 units 8 units 16 units

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in the given question. The following equation is given to us and we are told to find the radius of this circle. So what we can do first is we have the general equation of a circle. That is a standard equation. Standard equation of a circle of a circle is of the form x minus h whole squared plus y minus k. Hole squared is equal to r squared where the center of the circle would be at the coordinates hk. And the radius is given as our so the radius is given as art. So this is the standard form of a circle. So what we would do over here is we would change our convert the current equation that we have into this form. So in order to do that, let's first write the situation as x squared x squared minus 10 X. And we can see that first. What we can do is we can write 10 X as two times x times five. And the reason why we are writing this is that when we take the expansion of a minus b squared, it is of the form a squared minus two times eight times b times a plus b squared. So since this is the format that this is the expansion of a minus b squared, we are going to make this equation in that form so that we can write x minus some constants acquired in the in this equation as well. Right? So if we take a over here as X, we can write two times a times B. So we have taken B to be equal to five over here. Right? So we have to complete this square. We should be we should add A five square to this equation. Right? So five squared is 25. So let's add 25 and to keep the equation unchanged. We're just simply going to subtract 25 to. So now we are going to do the same thing with white. That is we are going to take in the equation. We have voice squared ah plus six Y. Which we are going to write as two times Y times three, which is six Y. So we have a two times a B. And then we take B to be equal to three. So we just take the square of three, which is nine. And we subtract nine as well. So what is left in the equation now? Now, Now, what is left is just 18? Right let's just look at the equation. Now we have taken x squared y squared. We have split 10 X 22 times five times X and 6522 times three times Why? What is left is just 18. So let's just write the 18 over here as well. It is plus 18. And this is equal to zero. So in the next step we are going to Group X squared minus two times x times five plus 25 as x minus five, whole squared. And we are going to group vice squared plus two Y plus two times y times three plus three squared as x plus three squared. Right and not X plus three squared Why? Plus three squared? Why? Plus three Squared? And now let's write this. So we have x minus five whole squared minus 25 plus Why? Plus three whole squared minus Myron Plus 18 is equal to zero. When we take -25 -9 plus 18 minus 25 minus nine. Iron Plus 18. What we get is -16. So we can write X -5 whole squared plus Y plus three whole squared minus 16 is equal to zero. Or we can write this equation as X -5 whole squared plus Y plus three squared is equal to 16. So 16 can be returned as four squared, right? And in the next step we right. The final form of this circle, the standard form of the circle as x minus five squared plus By -1 -3 Whole squared is equal to four squared. So now we can write the radius of the circle is equal to four. Right? Since it is in the form x minus h hold squared plus y minus uh G y minus k vote. It was the formula that we have wrote as y minus K. So it is in the form x minus h squared plus y minus k would be minus three. Whole squared is equal to four squared which is r squared. So r is the radius. So we had to find the radius over here, Which would be equal to four. So are as equal to four units as the required answer. I hope you understood the method that we have followed over here. Thank you.

What is the radius of a circle whose equation is x² y² 8x 6y 21 0 2 units 3 units 4 units 5 units?

What is the radius of a circle whose equation is x2 y2 − 10x 6y 18 0?

What is the radius of a circle whose equation is x2 y2?