Find expert advice and community support for all your questions on IDNLearn.com. Get the information you need quickly and accurately with our reliable and thorough Q&A platform.
Sagot :
Ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
- (A) 49x2 -98x + 64yz +256y -2,831 = 0
- (B) 81x2 -648x +100yz +200y -6,704 = 0
- (F) 64x2 +512x +81y2 -324y -3,836 = 0
What is an equation?
- An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.
- The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
To identify the ellipses:
For the standard-form equation of an ellipse: Ax^2+Bx+Cy^2+Dy+E=0
We can define:
- p=min(A,C)
- q=max(A,C)
Then the eccentricity can be shown to be:
- e=(1-p/q)
- p/q=1-e^2
For Eccentricity<0.5, we want:
- p/q>3/4
Checking the values of p/q for the given equations, we have p/q= equations (A), (B), and (F) are of ellipses with eccentricity < 0.5.
Therefore, ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
- (A) 49x2 -98x + 64yz +256y -2,831 = 0
- (B) 81x2 -648x +100yz +200y -6,704 = 0
- (F) 64x2 +512x +81y2 -324y -3,836 = 0
Know more about equations here:
https://brainly.com/question/22688504
#SPJ4
The complete question is given below:
Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
(A) 49x2 -98x + 64yz +256y -2,831=0
(B) 81x2 -648x +100yz +200y -6,704 =0
(C) 6x2 -12x +54y2 +108y -426 =0
(D) 49x2 + 196x +36y2 +216y -1,244 =0
(E) 4x +32x +25y2 - 250y +589 =0
(F) 64x2 +512x +81y2 -324y -3,836 =0
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.
