Find the Vertex Form 9x^2-4y^2=36

Problem

9*x2−4*y2=36

Solution

1. Identify the type of equation. This is the equation of a hyperbola because it contains both x2 and y2 terms with opposite signs.

2. Divide both sides of the equation by 36 to set the right side equal to 1.

(9*x2)/36−(4*y2)/36=36/36

3. Simplify the fractions by dividing the numerators and denominators by their greatest common factors.

(x2)/4−(y2)/9=1

4. Rewrite the denominators as squares to identify the values of a and b

(x2)/2−(y2)/3=1

5. Determine the vertex coordinates. Since there are no horizontal or vertical shifts (no h or k values subtracted from x or y, the center is (0,0) For a horizontal hyperbola of the form (x2)/(a2)−(y2)/(b2)=1 the vertices are located at (±a,0)

6. Calculate the vertices using a=2

Vertices=(±2,0)

Final Answer

(x2)/4−(y2)/9=1

Want more problems? Check here!