*equation of a hyperbola. Either the x coordinate or y coordinate is negative. The coordinate that is positive is the way that the hyperbola opens.If you have +x and -y, the hyperbola is going to open left-right because x coordinate is positive. Your a value always goes with your positive value (x or y) But unlike circles your a value ( is NOT always bigger than your b value.
*sketching the hyperbola.
find the centre of the hyperbola. It's just the opposite sign of what's inside the brackets.
find the values for a and b. You have to square root the denominator to get your values. You can trace your transverse and conjugate axes. You can find your vertecies which are the endpoints for transverse axis. The vertecies are your starting points for your hyperbola.
*we now have to find the equation of the asymptotes to make our sketch complete and where to draw the hyperbola. Equation of a line: y=mx+b.So, you know your x and y values, they're the values of the centre (x=-2,y=1). You know the m which is the slope. After you find your b values, you can draw your asymptotes equations with dotted lines and then draw your hyperbola.
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