Find the vertices the foci and the equations of the asymptot

Find the vertices, the foci, and the equations of the asymptotes of the hyperbola. y2 4x2 14y 24x + 9 = 0 vertices (x, y) = (smaller y-value) (x, y) = (larger y-value) foci (x, y) = (smaller y-value) (x, y) = (larger y-value) asymptotes (smaller slope) (larger slop

Solution

y^2 - 4x^2 -14 y -24x +9=0

y^2 -14y +49 -4(x^2 +6x + 9)=49 -36=13

(y-7)^2 /13 -(x+3)^2/(13/4)=1

center=(7,-3)

vertices =(7 , +- sqrt 13 -3)

focii=(h,k+-c) =(7 , -3 +-sqrt(65)/2)