Answered

Sumali sa IDNStudy.com at makuha ang mabilis at kaugnay na mga sagot. Alamin ang mga detalyadong sagot sa iyong mga tanong mula sa aming malawak na kaalaman sa mga eksperto.

what is the equation of the circle with diameter whose endpoints are (3,1) and (5.5)

Sagot :

UK2019idn

✏️CIRCLE EQUATION

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{QUESTION:}}[/tex]

  • What is the equation of the circle with diameter whose endpoints are (3,1) and (5,5)?

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex]\quad\Large\rm»\:\: \green{(x-4)^2+(y-3)^2=5}[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- The equation of the circle in standard form is written as:

  • [tex](x-h)^2+(y-k)²=r^2[/tex]

- Where (h,k) is the center and r is the radius.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

- Find the midpoint between the endpoints because that would be the center of the circle.

[tex] \begin{aligned}& \bold{ \color{lightblue}Formula:} \\& \boxed{M = \bigg(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigg)}\end{aligned}[/tex]

  • [tex] \begin{aligned}{Center = \bigg(\frac{3 + 5}{2},\frac{1 + 5}{2}\bigg)}\end{aligned}[/tex]

  • [tex] \begin{aligned}{Center = \bigg(\frac{8}{2},\frac{6}{2}\bigg)}\end{aligned}[/tex]

  • [tex]Center = (4, 3)[/tex]

- The center is at (4,3). Substitute in the standard form of the equation.

  • [tex](x - 4)^{2} + (y - 3)^{2} = {r}^{2} [/tex]

- Find the square of the radius if it passes through one of the given endpoints of the diameter: (5,5)

  • [tex](5 - 4)^{2} + (5 - 3)^{2} = {r}^{2} [/tex]

  • [tex](1)^{2} + (2)^{2} = {r}^{2} [/tex]

  • [tex]1 + 4 = {r}^{2} [/tex]

  • [tex]5 = {r}^{2} [/tex]

- Thus, the radius² is 5. Substitute the square of the radius to the equation.

  • [tex](x - 4)^{2} + (y - 3)^{2} = 5[/tex]

[tex]\therefore[/tex] (x - 4)² + (y - 3)² = 5 is the standard form of the equation.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#CarryOnLearning

Natutuwa kami na ikaw ay bahagi ng aming komunidad. Magpatuloy sa pagtatanong at pagbibigay ng mga sagot. Sama-sama tayong magtutulungan upang makamit ang mas mataas na antas ng karunungan. Bawat tanong ay may sagot sa IDNStudy.com. Salamat sa pagpili sa amin at sa muling pagkikita.