Medal and ! write equation: the hyperbola with center (1, 2), vertices (1, 5) and (1, –1) , and foci (1, 7) and (1, –3).

We notice the x of the foci don't change
that means the hyperbola opens up and down

hmm
center is (1,2) and vertices (1,5) and (1,-1)
the distance to a vertex is 3, that is 'a'
the rectangle of refernce is 6 units high
remember that
a²+b²=c² where a is major axis, b is minor axis and c is the distance from focs to center
from focus to center is 5 units
a is 3
3²+b²=5²
9+b²=25
mnus 9
b²=16
sqrt
b=4

so
is the equation

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c