SOLUTION: Can you help me with my homework, please? Here's the given problem: Reduce this equation to standarm form 9x^2-4y^2+36x-16y-16=0. Find also the coordinates of the center, foc

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Can you help me with my homework, please? Here's the given problem: Reduce this equation to standarm form 9x^2-4y^2+36x-16y-16=0. Find also the coordinates of the center, foc      Log On


   

Question 1006131: Can you help me with my homework, please?
Here's the given problem:
Reduce this equation to standarm form 9x^2-4y^2+36x-16y-16=0. Find also the coordinates of the center, foci, and vertices. Draw also the asymptote and sketch the graph of the equation.
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2-4y%5E2%2B36x-16y-16%22%22=%22%220

9x%5E2%2B36x-4y%5E2-16y-16%22%22=%22%220

9%28x%5E2%2B4x%29-4%28y%5E2%2B4y%29-16%22%22=%22%220

9%28x%5E2%2B4x%2B4-4%29-4%28y%5E2%2B4y%2B4-4%29%22%22=%22%2216

9%28%28x%2B2%29%5E2-4%29-4%28%28y%2B2%29%5E2-4%29%22%22=%22%2216

9%28x%2B2%29%5E2-36-4%28y%2B2%29%5E2%2B16%22%22=%22%2216

9%28x%2B2%29%5E2%22%22-%22%224%28y%2B2%29%5E2-20%22%22=%22%2216

9%28x%2B2%29%5E2%22%22-%22%224%28y%2B2%29%5E2%22%22=%22%2236

9%28x%2B2%29%5E2%2F36%22%22-%22%224%28y%2B2%29%5E2%2F36%22%22=%22%2236%2F36

%28x%2B2%29%5E2%2F4%22%22-%22%22%28y%2B2%29%5E2%2F9%22%22=%22%221

Compare with

%28x-h%29%5E2%2Fa%5E2%22%22-%22%22%28y-k%29%5E2%2Fb%5E2%22%22=%22%221

h=-2, k=-2, a=2, b=3, c=√(a^2+b^2)=√(2^2+3^2)=√(4+9)=√(13)}}}

center = (h,k), vertices = (h±a,k),  foci = (h±c,k)

center = (-2,-2), vertices = (-2±2,-2),  foci = (-2±√(13),-2)

Draw defining rectangle 2a wide, 2b high with center in middle.
Extend diagonals for asymptotes.  Foci are indicated as the little black
circles.



Edwin