Mathematics - Parabola Question with Solution | TestHub

The equation of tangent ($T=0$) would be$\frac{1}{2} \left(y+10\right)- 6=2x$

$4x-y+2=0$



The center of the circle is$(-4,1)$and the point of contact would be the foot of perpendicular from$(-4,1)$on$4x-y+2=0$

$\frac{\alpha +4}{4}=\frac{\beta -1}{-1}= -\left(\frac{-16-1+2}{4^2+1^2}\right)$

$\frac{\alpha +4}{4}=\frac{15}{17}$and$\frac{\beta -1}{-1}=\frac{15}{17}$

$\alpha = -\frac{8}{17}$,$\beta = \frac{-15}{17}+1=\frac{2}{17}$

Hence option$\left(-\frac{8}{17}, \frac{2}{17}\right)$is correct.