Question

Find equation of hyperbola given foci and vertices calculator

Answer 1

Equation of the hyperbola: x2−4y2=49 or x2−4y2−49=0.

Graph: to graph the hyperbola, visit hyperbola graphing calculator (choose the implicit option).

Standard form: x249−4y249=1.

Center: (0,0).

Vertices: (−7,0), (7,0).

Co-vertices: (0,−72)=(0,−3.5), (0,72)=(0,3.5).

Foci: (−75–√2,0)≈(−7.82623792124926,0), (75–√2,0)≈(7.82623792124926,0).

Eccentricity: 5–√2≈1.11803398874989.

Focal Parameter: 75–√10≈1.56524758424985.

Major axis length: 14.

Semimajor axis length: 7.

Minor axis length: 7.

Semiminor axis length: 72=3.5.

First asymptote: y=−x2=−0.5x

Second asymptote: y=x2=0.5x

First directrix: x=−145–√5≈−6.26099033699941.

Second directrix: x=145–√5≈6.26099033699941.

x-intercepts: (−7,0),(7,0).

No y-intercepts.