If the lines x + y = a and x – y = b touch the
curve y = x2
– 3x + 2 at the points where the
curve intersects the x-axis, then ${a \over b}$ is equal
to _______.
Answer (integer)
0
Solution
y = x<sup>2</sup>
– 3x + 2
<br><br>$\Rightarrow$ y = (x – 1)(x – 2)
<br><br>At x-axis y = 0
<br>$\Rightarrow$ x = 1, 2
<br><br>So this curve intersects the x-axis
at A(1, 0) and B(2, 0).
<br><br>${{dy} \over {dx}} = 2x - 3$
<br><br>${\left( {{{dy} \over {dx}}} \right)_{x = 1}} = - 1$ and ${\left( {{{dy} \over {dx}}} \right)_{x = 2}} = 1$
<br><br>Equation of tangent at A(1, 0) :
<br><br>y = –1(x –1)
<br><br>$\Rightarrow$ x + y = 1
<br><br>and equation of tangent at B(2, 0):
<br><br>y = 1(x – 2)
<br><br>$\Rightarrow$ x – y = 2
<br><br>So a = 1 and b = 2
<br><br>$\Rightarrow$ ${a \over b}$ = 0.5
About this question
Subject: Mathematics · Chapter: Application of Derivatives · Topic: Tangents and Normals
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