Question

Graph the hyperbola with equation quantity x minus 1 squared divided by 49 minus the quantity of y plus 3 squared divided by 9 equals 1.

Answer 1

See attached diagram

Explanation:

You are given the equation of hyperbola

`((x-1)^2)/(49)-((y+3)^2)/(9)=1`

From this equation,

• the center of hyperbola is at point (1,-3);
• the real semi-axes
  `a^2=49\Rightarrow a=7;`
• the imaginary semi-axes
  `b^2=9\Rightarrow b=3.`

Draw two parallel lines x=1 and y=-3 (they intersect at the center of hyperbola), then on horizontal line match two hyperbola's vertices (7 units to the left and 7 units to the right from the center). Then draw two branches of hyperbola (one in negative direction and one in positive direction).