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 4x2+y2=164x^2 + y^2 = 16.

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 4x2+y2=164x^2 + y^2 = 16.
  1. Divide by 1616: Divide both sides of the equation by 1616 to get the standard form.4x216+y216=1616\frac{4x^2}{16} + \frac{y^2}{16} = \frac{16}{16}
  2. Simplify fractions: Simplify the fractions. x24+y216=1\frac{x^2}{4} + \frac{y^2}{16} = 1
  3. Check standard form: Check the equation to ensure it's in standard form for an ellipse.\newlineThe standard form is (x2/a2)+(y2/b2)=1(x^2/a^2) + (y^2/b^2) = 1, where aa and bb are the lengths of the semi-major and semi-minor axes, respectively.

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 2 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 3 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 2 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 2 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 3 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 4 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 4 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 4 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 4 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 4 months ago

View all (29)