Q89 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Mathematics

If $f(x, y)=0$ is the combined equation of the lines joining the origin to the points where the line $4 x-6 y-2=0$ meets the curve $3 x^2-4 x y+5 y^2-2 x+y-6=0$, then $\frac{f(1,-1)}{f(-1,-1)}=$

  • Correct answer
    A
    153
  • B
    -153
  • C
    1
  • D
    -1

Solution

Given curve is $3 x^2-4 x y+5 y^2-2 x+y-6=0$ now equation of the combined lines joining the origin to the points where $4 x-6 y-2=0$ meets Let, homogenisation of the given curve from the line $$ \begin{aligned} & 4 x-6 y-2=0 \Rightarrow 1=2 x-3 y \\ & f(x, y)=3 x^2-4 x y+5 y^2-2 x(2 x-3 y)+y(2 x-3 y)-6(2 x \\ & -3 y)^2=0 \\ & =25 x^2-76 x y+52 y^2=0 \end{aligned} $$ Here, $\frac{\mathrm{f}(1,-1)}{\mathrm{f}(-1,-1)}=\frac{153}{1}=153$

Hence, the correct answer is option: 'A'.

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