I consider two curves $x^2=4ay$ and $x^2+y^2=\lambda^2$
So $$y^2+4ay-\lambda^2=0$$ And $$y_1+y_2\not =0$$
I just want to whether the question itself is right or not
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Are there any restrictions on $a$ and $\lambda$? – VIVID Mar 03 '21 at 14:43
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@VIVID As long as $a,\lambda$ are non-zero reals, they don't need any restrictions. – cosmo5 Mar 03 '21 at 14:47
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For $x^2=4ay$, sum of abscissae will be zero due to symmetry about y-axis.
For $y^2=4ax$, sum of ordinates will be zero due to symmetry about x-axis.
(Perhaps the question has been mixed up? Or was it originally a true/false question?)
cosmo5
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1Yeah that’s exactly what I thought. The question seems to be wrong here – Aditya Mar 03 '21 at 14:47
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The equation $y^2+4ay-\lambda^2=0$ has the solutions
$$y_{1/2}=-2a \pm \sqrt{4a^2+\lambda^2}.$$
Hence
$$y_1+y_2=-4a.$$
Fred
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