$4x^2 - 5y^2 - 16x - 50y + 71 = 0$
Thank you!
2026-04-06 10:42:33.1775472153
How would you find the eccentricity of this conic section?
73 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- Proving the differentiability of the following function of two variables
- If $f ◦f$ is differentiable, then $f ◦f ◦f$ is differentiable
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Number of roots of the e
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- How to prove $\frac 10 \notin \mathbb R $
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
Related Questions in CONIC-SECTIONS
- Show that the asymptotes of an hyperbola are its tangents at infinity points
- Do projective transforms preserve circle centres?
- A Problem Based on Ellipse
- Perfect Pascal Mysticum Points
- I need to rotate this parabola around the y axis, but can't find the correct expression
- Prove that the common chord passes through the origin.
- Rotated ellipse tangent to circle
- tangent to two different branches of the hyperbola
- Probability that a triangle inscribed in an ellipse contains one of its foci
- Locus of mid point of intercepts of tangents to a ellipse
Related Questions in POLAR-COORDINATES
- Second directional derivative of a scaler in polar coordinate
- polar coordinate subtitution
- $dr$ in polar co-ordinates
- Finding the centroid of a triangle in hyperspherical polar coordinates
- Arc length of polar function and x interceps
- Evaluation of $I=\iint_R e^{-(x^2+y^2)} \,dx\,dy$ by change of variable
- Finding area bound by polar graph
- Question about the roots of a complex polynomial
- Polar Area Integral with Absolute Function
- How to compute 'polar form' of a line given two points in cartesian coordinate system?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Rewriting this in standard form we get \begin{align*} 4x^2-5y^2-16x-50y+71 &= 4x^2-16x-5y^2-50y+71\\ &=4(x^2-4x)-5(y^2+10y)+71 \\ &= 4(x^2-4x+4)-16-5(y^2+10y+25)+125+71\\ &=4(x-2)^2-5(y+5)^2+180=0\\ &=4(x-2)^2-5(y+5)^2 = -180\\ &=5(y+5)^2-4(x-2)^2=180 \end{align*} Dividing both sides by $180$ we get $$\frac{(y+6)^2}{36}-\frac{(x-2)^2}{45} = 1$$ This is a hyperbola with $a=6, b=3\sqrt5$ so $c = \sqrt{36+45} = 9$. The eccentricity is given by $\dfrac{c}{a}$. So it is $\dfrac96 = \dfrac32$.