Q48 / 75 · JEE Main 2020 (05 Sep Shift 2) · Mathematics

If the lines $x + y = a$ and $x - y = b$ touch the curve $y = x^{2} - 3 x + 2$ at the points where the curve intersects the $x -$ axis, then $\frac{a}{b}$ is equal to $\dots$

Correct answer: 0.5

Solution

$y = x^{2} - 3 x + 2, x + y = a, x - y = b$

$\Rightarrow x^{2} - 3 x + 2 = 0$

$x_{1} = 2 x_{2} = 1$

Therefore, points are $(2, 0) (1, 0)$

$b = 2 a = 1$

$∴ \frac{a}{b} = \frac{1}{2} = 0.5$

Hence, the correct answer is 0.5.

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