FINDING VERTICES FOCI AND ASYMPTOTES OF HYPERBOLA WORKSHEET

Answer Key

1)  

Center : C (0, 0)

Vertices :  A(3, 0) and A'(-3, 0) and c = 5

Foci : F₁ (5, 0) and F₂ (-5, 0)

Equation of asymptotes :  y = (-4/3) and y = (4/3) x

2)

Center : C (0, 0)

Vertices :  A(10, 0) and A'(-10, 0) and c = 2√41

Foci : F₁ (2√41, 0) and F₂ (-2√41, 0)

Equation of asymptotes : y = (-4/5) and y = (4/5) x

3)

Center : C (0, 0)

Vertices : A(0, 4) and A'(0, -4) and c = 2√13

Foci : F₁ (0, 2√13) and F₂ (0, 2√13)

Equation of asymptotes : y = (-2/3)x  and y = (2/3) x

4)

Center : C (0, 0)

Vertices :  A (0, 1/2) and A'(0, -1/2) and c = √5/2

Foci : F₁ (0, √5/2) and F₂ (0, -√5/2)

Equation of asymptotes : y = (-1/2)x and y = (1/2) x

5)

Center : C (h, k) ==> (3, -3)

Vertices :  A(5, -3),  A'(1, -3) and c = √5

Foci : F₁ (3 + √5 , -3) and F₂ (3 - √5 , -3)

Equation of asymptotes :

y = (1/2)x - (9/2) and y = (-1/2)x + (-3/2)

6)

Center : C (h, k) ==> (1, -2)

Vertices : A(1, 0), A'(1, -4) and c = 2√5

Foci :F₁ (1, -2 + 2√5 ) and F₂ (1, -2 - 2√5)

Equation of asymptotes :

y = (1/2)x - (5/2) and y = (-1/2)x - (3/2)