JEE PYQ: Parabola Question 9
Question 9 - 2020 (05 Sep Shift 2)
If the lines $x + y = a$ and $x - y = b$ touch the curve $y = x^2 - 3x + 2$ at the points where the curve intersects the $x$-axis, then $\frac{a}{b}$ is equal to ______.
Show Answer
Answer: 0.5
Solution
Curve intersects $x$-axis at $A(1,0)$ and $B(2,0)$. $\frac{dy}{dx} = 2x - 3$: slope at $A = -1$, slope at $B = 1$. Tangent at $A$: $y = -(x-1) \Rightarrow x + y = 1$, so $a = 1$. Tangent at $B$: $y = (x-2) \Rightarrow x - y = 2$, so $b = 2$. $\frac{a}{b} = 0.5$.
BETA
