Question bank/JEE Main/Mathematics

JEE MainMathematicsModerateConic Sections

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

Show answer and solution
Let tangent be y=ax + b on solving with both curves and putting
D=0 gives
ekuk fd y=ax + b dks nksuksa oØksa ds lkFk gy djds D=0
a2+10a+4b+1=0 and a2−2a+4b−3=0⇒a=−1/3a^{2} + 10a + 4b + 1 = 0\ and\ a^{2} - 2a + 4b - 3 = 0 \Rightarrow a = - 1/3

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

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