For each given equation, please identify the center, vertex or vertices, focus or foci, and asymptotes. Finally sketch the graph. Equations are listed in the description.

Question

a) (x+6)^2 _ (y+5)^2 = 1

64 58

b) -4x^2 +3y^2 +72x -18y = 321

For b) also determine the eccentricity, if possible.

Answer 1

Hi Lexi

Review the format of the equations, for example Equation a) looks like a Hyperbola you can look up the Equations of a Hyperbola online or in your text. Since all the values are given you can assign values to a², b², c², h, and k, do take a look. You should also be able to calculate e, vertices, foci

In general a Hyperbola = (x²/a²) - (y²/b² )= 1 this is when the center is at zero for a sideways or horizontal hyperbola

When the center is not at zero

((x -h)²/a²) - ((y - k)²/b²) = 1, for hyperbola along the x axis for sideways

There is also a vertical hyperbola but you can look this up too.

But if you look up the hyperbola you will most likely only need to plug in some given values especially in a)

a)((x+6)²/64 - (y+5)²/58) =1

Against the format

((x -h)²/a²) - ((y - k)²/b²) = 1

Please give it a try

Also you can graph them at Desmos.com to see and confirm your numbers

For b) you will need to complete the squares first, if that is done correctly again values for the variables will be available and you just need to plug them into the appropriate Hyperbola equation. b) reads like a vertical hyperbola because the coefficient of x² is negative.

I hope this helps please send a message if you need further help.

Remember graphing your equations can serve as both a check and a guide for your variables.