Question bank/JEE Main/Mathematics

The gradient of the common tangent to the two curves, y=x^2 -
5x + 6 and y = x^2 + x + 1is
nks oØksa y=x^2 - 5x + 6 rFkk y = x^2 + x + 1

A$2x - 3y + 5 = 0$B$3x + 2y + 14 = 0$C$3x + 2y + 5 = 0$D$2x - 3y + 14 = 0$

Show answer and solution▾

∴ ekuk $z(\alpha,\beta)$
$\therefore\frac{\alpha + 2}{2} = - 1,\frac{\beta + 3}{2} = 1$
$\alpha = - 4,\beta = - 1$
$\therefore z( - 4, - 1)\$ Slope of VS dh izo.krk
$= \frac{3 - 1}{2 + 1} = \frac{2}{3}$
∴Equation of directrix is lehdj.k
$y + 1 = - \frac{3}{2}(x + 4)$
$\Rightarrow 2y + 2 = - 3x - 12$ $\Rightarrow 3x + 2y + 14 = 0$

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx