Question 1142075
<br>
{{{x^2/81-y^2/49 = 1}}}<br>
{{{(x-0)^2/9^2-(y-0)^2/7^2 = 1}}}<br>
{{{(x-0)^2/a^2-(y-0)^2/b^2 = 1}}}<br>
The center of the hyperbola is (0,0).<br>
The x squared term is positive, so the branches open right and left.<br>
The length of the transverse axis (in the x direction, between the two vertices) is 2*a = 2*9=18; the length of the conjugate axis (the perpendicular bisector of the transverse axis) is 2*b = 2*7=14.<br>
To sketch the hyperbola, draw a rectangle with the ends of the transverse and conjugate axes as the midpoints of the sides of the rectangle.  The diagonals of that rectangle are the asymptotes of the hyperbola.<br>
a is the distance from the center to each vertex.<br>
c is the distance from the center to each focus, where c^2 = a^2+b^2.<br>
That should give you all the information you need to answer the questions.