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 with center at the origin, vertex (0,9)(0,9), and co-vertex (−8,0)(-8,0).

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Write equations of ellipses in standard form using propertiesright chevron icon

Full solution

Q. Write the equation in standard form for the ellipse with center at the origin, vertex (0,9)(0,9), and co-vertex (−8,0)(-8,0).
  1. Identify Orientation of Ellipse: Identify the orientation of the ellipse.\newlineSince the vertex is (0,9)(0,9) which is on the yy-axis, the ellipse is vertical.
  2. Find Value of 'a': Find the value of 'a'.\newlineThe vertex is (0,9)(0,9), so 'a' is the distance from the center to the vertex along the y-axis.\newlinea=9a = 9
  3. Find Value of 'b': Find the value of 'b'.\newlineThe co-vertex is (−8,0)(-8,0), so 'b' is the distance from the center to the co-vertex along the x-axis.\newlineb=8b = 8
  4. Write Equation in Standard Form: Write the equation of the ellipse in standard form.\newlineThe standard form for a vertical ellipse is (x−h)2/b2+(y−k)2/a2=1(x-h)^2/b^2 + (y-k)^2/a^2 = 1, where (h,k)(h,k) is the center.\newlineSince the center is at the origin (0,0)(0,0), the equation becomes:\newlinex2/b2+y2/a2=1x^2/b^2 + y^2/a^2 = 1\newlineSubstitute ′a′'a' and ′b′'b' into the equation:\newlinex2/82+y2/92=1x^2/8^2 + y^2/9^2 = 1
  5. Simplify the Equation: Simplify the equation. x264+y281=1\frac{x^2}{64} + \frac{y^2}{81} = 1

More problems from Write equations of ellipses in standard form using properties

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 (39)