Mathematics Tes...

The locus of the mid point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

If the planes $\overrightarrow{r}.\left(2\widehat{i}-\lambda \widehat{j}+3\widehat{k}\right)=0$ and $\overrightarrow{r}.\left(\lambda \widehat{i}+5\widehat{j}-\widehat{k}\right)=5$ are perpendicular to each other, then the value of ${\mathrm{\lambda }}^2+\mathrm{\lambda }$ is

If $x \frac{dy}{dx}=y(\log y-\log x+1)$, then the solution of the equation is