AP EAMCET2016MathematicsEllipse

The equations of the latusrectum of the ellipse 9 x^2+25 y^2-36 x+50 y-164=0 are

Options

Ax-4=0, x+2=0
Bx-6=0, x+2=0
Cx+6=0, x-2=0
Dx+4=0, x+5=0

Correct answer

B. x-6=0, x+2=0

Step-by-step solution

We have, aligned & 9 x^2+25 y^2-36 x+50 y-164=0 & 9 x^2-36 x+36++25 y^2+50 y-25=164+36+25 & 9 (x^2-4 x+4 )-25 (y^2+2 y-1 )=225 & 9(x-2)^2-25(y+1)^2=225 aligned aligned & (x-2)^2 25 + (y+1)^2 9 =1 & Eccentricity e = 1- ( b a )^2 & = 1- 9 25 = 4 5 aligned Equation of the latusrectum, aligned & x-2= a e & x-2= 5 4 5 = 4 & x= 4+2 & x=6 and x=-2 & x-6=0, x+2=0 aligned

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