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Find the standard form of the equation of the circle with endpoints of a diameter at the points (7,8) and ( - 9,2). Type the standard form of the equation of this c...

Question

Find the standard form of the equation of the circle with endpoints of a diameter at the points (7,8) and ( - 9,2). Type the standard form of the equation of this circle.(Type a equation )

Find the standard form of the equation of the circle with endpoints of a diameter at the points (7,8) and ( - 9,2). Type the standard form of the equation of this circle. (Type a equation )



Answers

Write the standard form of the equation of the circle with the given characteristics. Endpoints of a diameter: (0,0),(6,8)

Okay, in this case was simply need to find the equation off circle. We have been given that in point off diameter in this open is given one comma minus seven. Right, Andi nine comma minus five. So four thing is very clear that the center co ordinate with the verge of this court. Next, events of one bless nine by two on minus seven minus fight back. Because that central light the midpoint off this in part of the diamond does have sent the coordinators 10 by two, which is five on minus tool. But do it is minus six, right? The two points are I'm just as human as one in minus seven on nine and minus five as the end point of the diamond. Right now the circle passes through this point B Q and we know that the question of circle is X minus its hold square less by minus. Kehoe it square. Is it wise to our square? So this buoyant will always decide this fire. The equation of the circle sent to this five and minus 61 minus five squid If I just can't see the point B White. So why in this good becomes minus seven and keys minus six. So this becomes plastics will square because minus minus is plus, that is a close to our square. So this simply comes out with 16 plus, um, minus seven, which is one that is eclipsed, Wallace. But so from here, I get them. I live are square. Right. So are square is equivalent to 70. No, the question of circle finally will be here. We have center, which is a five in minus X rays. So eggs minus five squared, plus by plus six square. That is a close to 70. All right.

In this question, we have to find standard form off an equation off a circle with end points off diameter at one comma for and my last re coma to now for writing the standard form of an equation. We need Sankaran Radius off the circle as it is X minus h old square. Bless y minus K hold square is equal to R squared. We're at school. McKay's the center and odd is that radius. Now, as we know, center is midpoint off that diameter. Therefore, we can find midpoint using the formula X one plus x two Divided by two comma violent plus y two Divided by two We're x one and x two r X coordinates off the points and vibrant and by two are the by coordinates off the given points. Hence center will be at one plus minus three, divided by two comma four plus two divided by two. Now, by simply find this, we will get minus one comma three. Hence, the center of the circle will be at minus one comma tree. Now we have to find radius off the circle, and we know radius is distance between centre and any point off the circle. So by using the distance formula, we can find distance between minus one comma tree and one comma four that will be equal to the square root off one minus minus one that will be one plus one whole square, plus four minus three whole square. No, By simply find this, we will get square root off. One plus one is two and square off. Two is four plus four minus trees. One and square of one is one again. Therefore the rest will be equal to square root off. Five. No putting the values off Etch K and R In this equation, we will get standard form off any creation that will be X plus one whole square. Bless y minus three hold square is equipped, toe are square and value of artists square it off five and it's square will be five

In this question, we have to find standard form of an equation off a circle with end points off a diameter at four comma three and zero comma one now for writing the standard form of an equation. Village center and radius off the circle as standard form is X minus. H hold square plus y minus K hold square is equal to our square were at school. McKay's, the center and R is the radius and we know sank. There is the midpoint off Die Diameter. Therefore, we confined midpoint off the diameter, using the formula x one plus x two divided by two coma Why even plus why toe divided by two Now we will use this formula to find the center of the circle. Hence, center will be it four plus zero, divided by two that will be to coma three plus one divided by two, which is again, too. Hence, center off the circle is act Okamoto, as we know the area sees distance between centre and any point on the circle. Therefore, by using that distance formula, we can find distance between center that is to cometo and any point which is given to us Let's take zero comma one. Therefore radius will be equal to square wrote off to minus zero whole square. That will be four plus two minus one whole square. That will be one. Hence. Radius is equal to the square. Root off five now putting the values off Etch K and R In this equation, we will get X minus two. Hold square plus via I minus to hold square is equate o r squared. Were value of artists credit off five. Therefore it's square will be five.

Okay, here we have a sketch of the graph, and we can see from the sketch that the center of the circle is the point to negative one. We can also see that the radius is to so we can substitute those numbers into the standard form equation of the circle. The center gives us A and B, and the radius gives us our So we have X minus two quantity squared. Plus why minus negative. One quantity squared equals two squared. And we'll just simplify that and we get X minus two quantity squared, plus why, plus one quantity squared equals four.


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