Q. What is the center of the hyperbola (144x2)−(81y2)=1?(_____,_____)
Standard Form of Hyperbola: The standard form of a hyperbola centered at (h,k) is either a2(x−h)2−b2(y−k)2=1 for a horizontal hyperbola or a2(y−k)2−b2(x−h)2=1 for a vertical hyperbola. We need to compare the given equation with the standard form to find the values of h and k, which represent the center of the hyperbola.
Comparing with Standard Form: The given equation is (144x2−81y2=1). We can rewrite this as (144(x−0)2−81(y−0)2=1) to make it look more like the standard form. From this, we can see that h=0 and k=0, since there are no terms to shift the x and y values in the equation.
Finding the Center: Since we have found that h=0 and k=0, the center of the hyperbola is at the point (0,0).