Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A circle in the xy-plane has the equation x^(2)+y^(2)-6x-10 y=2. What is the diameter of the circle?

A circle in the xy x y -plane has the equation x2+y2−6x−10y=2 x^{2}+y^{2}-6 x-10 y=2 . What is the diameter of the circle?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Geometryright chevron icon
Find properties of circles from equations in general formright chevron icon

Full solution

Q. A circle in the xy x y -plane has the equation x2+y2−6x−10y=2 x^{2}+y^{2}-6 x-10 y=2 . What is the diameter of the circle?
  1. Write Equation: Write down the given equation of the circle.\newlineThe given equation is x2+y2−6x−10y=2x^{2} + y^{2} - 6x - 10y = 2. We need to complete the square for both xx and yy to bring the equation into the standard form of a circle's equation, which is (x−h)2+(y−k)2=r2(x - h)^{2} + (y - k)^{2} = r^{2}, where (h,k)(h, k) is the center of the circle and rr is its radius.
  2. Rearrange and Group: Rearrange the equation and group xx's and yy's together.\newlineRearrange the equation as follows: x2−6x+y2−10y=2x^{2} - 6x + y^{2} - 10y = 2. This step is necessary to prepare for completing the square for both xx and yy terms.
  3. Complete X Square: Complete the square for the x terms.\newlineTo complete the square for x2−6xx^{2} - 6x, we take half of the coefficient of xx, which is −6/2=−3-6/2 = -3, square it, (−3)2=9(-3)^{2} = 9, and add and subtract it inside the equation. So, we get x2−6x+9−9x^{2} - 6x + 9 - 9.
  4. Complete Y Square: Complete the square for the y terms.\newlineSimilarly, for y2−10yy^2 - 10y, we take half of the coefficient of yy, which is −10/2=−5-10/2 = -5, square it, (−5)2=25(-5)^2 = 25, and add and subtract it inside the equation. So, we get y2−10y+25−25y^2 - 10y + 25 - 25.
  5. Rewrite and Simplify: Rewrite the equation with completed squares and simplify.\newlineAfter completing the squares, the equation becomes x2−6x+9+y2−10y+25=2+9+25x^{2} - 6x + 9 + y^{2} - 10y + 25 = 2 + 9 + 25. Simplify the right side: 2+9+25=362 + 9 + 25 = 36. The equation now is (x−3)2+(y−5)2=36(x - 3)^{2} + (y - 5)^{2} = 36.
  6. Identify Radius: Identify the radius of the circle.\newlineFrom the equation (x−3)2+(y−5)2=36(x - 3)^{2} + (y - 5)^{2} = 36, we see that the right side, 3636, represents r2r^{2}, where rr is the radius of the circle. Therefore, r=36=6r = \sqrt{36} = 6.
  7. Calculate Diameter: Calculate the diameter of the circle.\newlineThe diameter of a circle is twice its radius. Therefore, the diameter =2×r=2×6=12= 2 \times r = 2 \times 6 = 12.

More problems from Find properties of circles from equations in general form

Question
Write the equation in standard form for the circle with radius 1111 centered at the origin. ______
Get tutor helpright-arrow

Posted 2 months ago

Question
(x+55)2+(y−11.5)2=121 (x+55)^{2}+(y-11.5)^{2}=121 \newlineA circle in the xy x y -plane has the equation shown. What is the length of the diameter of the circle?
Get tutor helpright-arrow

Posted 2 months ago

Question
(y−45)2+(x+710)2=30 \left(y-\frac{4}{5}\right)^{2}+\left(x+\frac{7}{10}\right)^{2}=30 \newlineA circle in the xy x y -plane has the equation. What is the radius of the circle? Round the answer to the nearest tenth.
Get tutor helpright-arrow

Posted 1 month ago

Question
(x−17)2+(y−19)2=49 (x-17)^{2}+(y-19)^{2}=49 \newlineA circle in the xy x y -plane has the equation shown. How long is the radius of the circle?
Get tutor helpright-arrow

Posted 2 months ago

Question
x2+y2−6x+14y=6 x^{2}+y^{2}-6 x+14 y=6 \newlineWhat is the length of the diameter of the circle whose equation is shown?
Get tutor helpright-arrow

Posted 10 days ago

Question
A circle in the xy x y -plane has the equation\newlinex2+y2−10x+32y+272=0.  x^{2}+y^{2}-10 x+32 y+272=0 \text {. } \newlineWhich of the following best describes the location of the center of the circle and the length of its radius?\newlineChoose 11 answer:\newline(A) Center: (10,−32) (10,-32) \newlineRadius: 417 4 \sqrt{17} \newline(B) Center: (−10,32) (-10,32) \newlineRadius: 417 4 \sqrt{17} \newline(C) Center: (−5,16) (-5,16) \newlineRadius: 33\newline(D) Center: (5,−16) (5,-16) \newlineRadius: 33
Get tutor helpright-arrow

Posted 2 months ago

Question
A circle in the xy x y -plane has the equation\newline2x2+2y2−8x−5y−558=0.  2 x^{2}+2 y^{2}-8 x-5 y-\frac{55}{8}=0 \text {. } \newlineWhat is the diameter of the circle?
Get tutor helpright-arrow

Posted 20 days ago

Question
x2+y2−12x−10y+36=0 x^{2}+y^{2}-12 x-10 y+36=0 \newlineWhat is the length of the radius of the circle whose equation is shown?
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the center of the circle x2+y2−19y+26=0x^2+y^2-19y+26=0? \newline Simplify any fractions. \newline (□,□)(\square, \square)
Get tutor helpright-arrow

Posted 2 months ago

Question
Khan Academy\newlineLímites por susti\newlineGoogle\newlinePuede que necesites:\newlinelim⁡x→2(x3−5x2+1)= \lim _{x \rightarrow 2}\left(x^{3}-5 x^{2}+1\right)= \newlineEsconder calculadora\newlineCalculadora
Get tutor helpright-arrow

Posted 23 hours ago

View all (24)