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:

What is the center of the ellipse 8x2+y2−56=08x^2 + y^2 - 56 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find properties of ellipses from equations in general formright chevron icon

Full solution

Q. What is the center of the ellipse 8x2+y2−56=08x^2 + y^2 - 56 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(______,______)
  1. Divide by 5656: Divide the entire equation by 5656 to get the standard form of the ellipse equation.\newline(8x256)+(y256)=5656(\frac{8x^2}{56}) + (\frac{y^2}{56}) = \frac{56}{56}
  2. Simplify equation: Simplify the equation by reducing fractions. x27+y256=1\frac{x^2}{7} + \frac{y^2}{56} = 1
  3. Identify center: Identify the center of the ellipse by comparing to the standard form (x−h)2/a2+(y−k)2/b2=1(x-h)^2/a^2 + (y-k)^2/b^2 = 1. The center (h,k)(h,k) is at (0,0)(0,0) since there are no terms to shift the ellipse left/right or up/down.

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

Question
Write the equation in standard form for the ellipse with center at the origin, vertex (−10,0)(-10,0), and co-vertex (0,3)(0,3).
Get tutor helpright-arrow

Posted 7 months ago

Question
Write the equation in standard form for the ellipse 7x2+y2=217x^2 + y^2 = 21.\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the center of the ellipse x2+2y2−16=0x^2 + 2y^2 - 16 = 0?\newlineWrite your answer in simplified, rationalized form.\newline(_____,_____)(\_\_\_\_\_,\_\_\_\_\_)
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the length of the major axis of the ellipse x29+y22=1\frac{x^2}{9} + \frac{y^2}{2} = 1?\newlineWrite your answer in simplified, rationalized form.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the center of the ellipse ((x−5)29)+((y−2)254)=1\left(\frac{(x - 5)^2}{9}\right) + \left(\frac{(y - 2)^2}{54}\right) = 1?\newlineWrite your answer in simplified, rationalized form.\newline(________ , _______)
Get tutor helpright-arrow

Posted 9 months ago

Question
The equation of an ellipse is given below.\newline(x+15)2676+(y−4)2100=1 \frac{(x+15)^{2}}{676}+\frac{(y-4)^{2}}{100}=1 \newlineWhat are the foci of this ellipse?\newlineChoose 11 answer:\newline(A) (−15+24,4) (-15+\sqrt{24}, 4) and (−15−24,4) (-15-\sqrt{24}, 4) \newline(B) (−15,4+24) (-15,4+\sqrt{24}) and (−15,4−24) (-15,4-\sqrt{24}) \newline(C) (−39,4) (-39,4) and (9,4) (9,4) \newline(D) (−15,28) (-15,28) and (−15,−20) (-15,-20)
Get tutor helpright-arrow

Posted 9 months ago

Question
The equation of an ellipse is given below.\newline(x−5)23+(y−7)26=1 \frac{(x-5)^{2}}{3}+\frac{(y-7)^{2}}{6}=1 \newlineWhat are the foci of this ellipse?\newlineChoose 11 answer:\newline(A) (5,7+3) (5,7+\sqrt{3}) and (5,7−3) (5,7-\sqrt{3}) \newline(B) (−5,−7+3) (-5,-7+\sqrt{3}) and (−5,−7−3) (-5,-7-\sqrt{3}) \newline(C) (−5+3,−7) (-5+\sqrt{3},-7) and (−5−3,−7) (-5-\sqrt{3},-7) \newline(D) (5+3,7) (5+\sqrt{3}, 7) and (5−3,7) (5-\sqrt{3}, 7)
Get tutor helpright-arrow

Posted 9 months ago

Question
The equation of an ellipse is given below.\newlinex246+(y+8)226=1 \frac{x^{2}}{46}+\frac{(y+8)^{2}}{26}=1 \newlineWhat are the foci of this ellipse?\newlineChoose 11 answer:\newline(A) (0+20,8) (0+\sqrt{20}, 8) and (0−20,8) (0-\sqrt{20}, 8) \newline(B) (0,8+20) (0,8+\sqrt{20}) and (0,8−20) (0,8-\sqrt{20}) \newline(C) (0,−8+20) (0,-8+\sqrt{20}) and (0,−8−20) (0,-8-\sqrt{20}) \newline(D) (0+20,−8) (0+\sqrt{20},-8) and (0−20,−8) (0-\sqrt{20},-8)
Get tutor helpright-arrow

Posted 9 months ago

Question
Write an equation for an ellipse centered at the origin, which has foci at (±12,0) ( \pm 12,0) and vertices at (±13,0) ( \pm 13,0) .
Get tutor helpright-arrow

Posted 9 months ago

Question
Write an equation for an ellipse centered at the origin, which has foci at (0,±6) (0, \pm 6) and vertices at (0,±37) (0, \pm \sqrt{37}) .
Get tutor helpright-arrow

Posted 9 months ago

View all (53)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant