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:

Write the equation in standard form for the ellipse x2+6y2−18=0x^2 + 6y^2 - 18 = 0.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Convert equations of ellipses from general to standard formright chevron icon

Full solution

Q. Write the equation in standard form for the ellipse x2+6y2−18=0x^2 + 6y^2 - 18 = 0.
  1. Divide by 1818: Now, divide each term by 1818 to get the standard form of the ellipse. x218+6y218=1818\frac{x^2}{18} + \frac{6y^2}{18} = \frac{18}{18}
  2. Simplify the equation: Simplify the equation by reducing the fractions. x218+y23=1\frac{x^2}{18} + \frac{y^2}{3} = 1
  3. Fix previous mistake: Oops, I made a mistake in the previous step. I should have divided 6y26y^2 by 1818 correctly.\newlineLet's fix that.\newline(x2)/18+(6y2)/18=1(x^2)/18 + (6y^2)/18 = 1\newline(x2)/18+(y2)/3=1(x^2)/18 + (y^2)/3 = 1

More problems from Convert equations of ellipses from general to standard 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 (29)

Related topics

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