Identify Type of Equation: Identify the type of equation. x² + 4y² = 5 is an ellipse equation. Check for Real Solutions: Check if the equation can be solved for real values. Since the coefficients of x² and 4y² are positive, and the right side of the equation is positive (5), real solutions exist. Simplify to Standard Form: Simplify the equation to see the form of the ellipse. Divide each term by 5: x²/5 + 4y²/5 = 1 This simplifies to: (x²/5) + (4y²/5) = 1 Further simplification gives: (x²/5) + (y²/1.25) = 1 This is the standard form of an ellipse equation.

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$x^2 + 4y^2 = 5$

View step-by-step help

Home

Math Problems

Grade 6

Add, subtract, multiply, or divide two integers

Full solution

x^2 + 4y^2 = 5

Identify Type of Equation: Identify the type of equation. $x^2 + 4y^2 = 5$ is an ellipse equation.
Check for Real Solutions: Check if the equation can be solved for real values. Since the coefficients of $x^2$ and $4y^2$ are positive, and the right side of the equation is positive ( $5$ ), real solutions exist.
Simplify to Standard Form: Simplify the equation to see the form of the ellipse. Divide each term by $5$ : $\frac{x^2}{5} + \frac{4y^2}{5} = 1$ This simplifies to: $\left(\frac{x^2}{5}\right) + \left(\frac{4y^2}{5}\right) = 1$ Further simplification gives: $\left(\frac{x^2}{5}\right) + \left(\frac{y^2}{1.25}\right) = 1$ This is the standard form of an ellipse equation.