Calculate the center vertices foci and covertices and use th

Calculate the center, vertices, foci, and co-vertices and use them to make a sketch of each of the following hyperbolas - be sure to sketch the oblique asymptotes with dotted lines: (x - 4)^2/25 - (y - 2)^2/64 = 1 center point: ____________ focus points: ____________ vertex points: ____________ co-vertex points: _____________ y^2 - 4x^2 - 16x - 2y = 19 center point: ___________ focus points: ___________ vertex points: ___________ co-vertex points: ___________

Solution

(x-4)^2/25 - (y-2)^2/64=1

If we compare it with (x-h)^2/a^2 - (y-k)^2/b^2=1

we get centre=(4,2)

c^2-a^2=b^2, c^2= 25+64=89   c=sqrt89

Therefore the focii is at either side of the centre that is (4+sqrt89,2) and (4-sqrt89,2)

And since vertex is 5 units to either side of the centre

Therefore vertex = (4+5,2) and (4-5,2)=(9,2) and (-1,0)

covertex= (h,k+b) and (h,k-b)=(4,2+8) and (4,2-8)= (4,10 ) and (4,-6)