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 2x^(2)+2y^(2)-8x-5y-(55)/(8)=0". " What is the diameter of the circle?

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?

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\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?
  1. Rewrite Equation: Rewrite the given equation of the circle in a more standard form by completing the squares for xx and yy. \newline2x2+2y2−8x−5y−558=02x^2 + 2y^2 - 8x - 5y - \frac{55}{8} = 0 \newlineDivide the entire equation by 22 to simplify the coefficients of x2x^2 and y2y^2. \newlinex2+y2−4x−52y−5516=0x^2 + y^2 - 4x - \frac{5}{2}y - \frac{55}{16} = 0
  2. Complete Squares: Complete the square for the xx-terms.\newlineAdd (42)2=4\left(\frac{4}{2}\right)^2 = 4 to both sides of the equation to complete the square for xx.\newlinex2−4x+4+y2−(52)y−(5516)=4x^2 - 4x + 4 + y^2 - \left(\frac{5}{2}\right)y - \left(\frac{55}{16}\right) = 4
  3. Combine Terms: Complete the square for the yy-terms.\newlineAdd ((52)2)2\left(\frac{\left(\frac{5}{2}\right)}{2}\right)^2 = 2516\frac{25}{16} to both sides of the equation to complete the square for yy.\newlinex2−4x+4+y2−52y+2516−5516=4+2516x^2 - 4x + 4 + y^2 - \frac{5}{2}y + \frac{25}{16} - \frac{55}{16} = 4 + \frac{25}{16}
  4. Identify Radius: Combine like terms and rewrite the equation in standard form.\newline(x−2)2+(y−54)2=4+2516+5516(x - 2)^2 + (y - \frac{5}{4})^2 = 4 + \frac{25}{16} + \frac{55}{16}\newline(x−2)2+(y−54)2=4+8016(x - 2)^2 + (y - \frac{5}{4})^2 = 4 + \frac{80}{16}\newline(x−2)2+(y−54)2=4+5(x - 2)^2 + (y - \frac{5}{4})^2 = 4 + 5\newline(x−2)2+(y−54)2=9(x - 2)^2 + (y - \frac{5}{4})^2 = 9
  5. Identify Radius: Identify the radius of the circle from the standard form equation.\newlineThe standard form of a circle's equation 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 the radius.\newlineFrom the equation (x−2)2+(y−54)2=9(x - 2)^2 + (y - \frac{5}{4})^2 = 9, we can see that the radius rr is the square root of 99, which is 33.
  6. Calculate Diameter: Calculate the diameter of the circle using the radius.\newlineThe diameter DD of a circle is twice the radius, so D=2rD = 2r.\newlineD=2×3=6D = 2 \times 3 = 6

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 x2+y2−6x−10y=2 x^{2}+y^{2}-6 x-10 y=2 . What is the diameter of the circle?
Get tutor helpright-arrow

Posted 1 month 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
1.5361.536 divided 9696
Get tutor helpright-arrow

Posted 24 hours ago

View all (24)