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x2+4y2=5x^2 + 4y^2 = 5

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Add, subtract, multiply, or divide two integersright chevron icon

Full solution

Q. x2+4y2=5x^2 + 4y^2 = 5
  1. Identify Type of Equation: Identify the type of equation. x2+4y2=5x^2 + 4y^2 = 5 is an ellipse equation.
  2. Check for Real Solutions: Check if the equation can be solved for real values. Since the coefficients of x2x^2 and 4y24y^2 are positive, and the right side of the equation is positive (55), real solutions exist.
  3. Simplify to Standard Form: Simplify the equation to see the form of the ellipse. Divide each term by 55:x25+4y25=1\frac{x^2}{5} + \frac{4y^2}{5} = 1This simplifies to:(x25)+(4y25)=1\left(\frac{x^2}{5}\right) + \left(\frac{4y^2}{5}\right) = 1Further simplification gives:(x25)+(y21.25)=1\left(\frac{x^2}{5}\right) + \left(\frac{y^2}{1.25}\right) = 1This is the standard form of an ellipse equation.

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