Ask Question
8 October, 04:01

Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y minus 5 squared divided by 16 = 1

+3
Answers (1)
  1. 8 October, 05:25
    0
    Vertices at (-7, 5) and (-1, 5).

    Foci at (-9, 5) and (1,5).

    Step-by-step explanation:

    (x + 4) ²/9 - (y - 5) ²/16 = 1

    The standard form for the equation of a hyperbola with centre (h, k) is

    (x - h²) / a² - (y - k) ²/b² = 1

    Your hyperbola opens left/right, because it is of the form x - y.

    Comparing terms, we find that

    h = - 4, k = 5, a = 3, y = 4

    In the general equation, the coordinates of the vertices are at (h ± a, k).

    Thus, the vertices of your parabola are at (-7, 5) and (-1, 5).

    The foci are at a distance c from the centre, with coordinates (h ± c, k), where c² = a² + b².

    c² = 9 + 16 = 25, so c = 5.

    The coordinates of the foci are (-9, 5) and (1, 5).

    The Figure below shows the graph of the hyperbola with its vertices and foci.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y minus 5 squared ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers