Question : Find the coordinates of the centre,foci and equation of directrix of the hyperbola x2-3y2-4x=8 - Maths - Three Dimensional Geometry

Question

Question : Find the coordinates of the centre,foci and
equation of directrix of the hyperbola x 2 - 3 y 2 - 4 x = 8

Shruti Tyagi · Accepted Answer

Dear Student,

x2-3y2-4x=8⇒x2-3y2-4x+4=8+4⇒x2-4x+4-3y2=12⇒x-22-3y2=12⇒x-2212-3y212=1⇒x-2212-y24=1this is general equation of hyperbolax-h2a2-y-k2b2=1where h=2,k=0 a2=12⇒a=23 and b=2Now centre of this hyperbola=h,k=2,0Now calculate eccentricity of hyperbolab2=a2e2-14=12×e2-1⇒13=e2-1⇒e2=1+13⇒e2=43⇒e=±23Now foci of the hyperbola=ae,0therefore foci=23×23,0 and -23×23,0 =4,0 and -4,0 Now equation of directrix is given by x=±ae⇒x=±2323⇒x=±3×3⇒x=±3
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Question : Find the coordinates of the centre,foci and equation of directrix of the hyperbola x 2 - 3 y 2 - 4 x = 8

Question : Find the coordinates of the centre,foci and equation of directrix of the hyperbola $x^{2} - 3 y^{2} - 4 x = 8$