find the equation to the ellipse whose axes are of lengths 6 and 2*(root 6) and their equations are x-3y+3=0 - Maths - Conic Sections

Question

find the equation to the ellipse whose axes are of lengths 6 and
2*(root 6) and their equations are x-3y+3=0 and 3x+y-1=0
respectively

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:
We have,2a=6 or a=62=3 and2b=26 or b=262=6Now, the required equation of ellipse isx-3y+3232=3x+y-1262⇒x2+9y2+9-6xy-18y+6x9=9x2+y2+1+6xy-2y-6x6⇒x2+9y2+9-6xy-18y+6x3=9x2+y2+1+6xy-2y-6x2⇒2x2+9y2+9-6xy-18y+6x=39x2+y2+1+6xy-2y-6x⇒2x2+18y2+18-12xy-36y+12x=27x2+3y2+3+18xy-6y-18x⇒25x2-15y2-15+30xy+30y-30x=0

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find the equation to the ellipse whose axes are of lengths 6 and 2*(root 6) and their equations are x-3y+3=0 and 3x+y-1=0 respectively.