If y = mx + 4 is a tangent to both the parabolas, y2 = 4x and x2 = 2by, then b is equal to :
Solution
Given y = mx + 4 is tangent to both the parabolas.
<br><br>$\therefore$ Applying condition of tangent
for y<sup>2</sup>
= 4x, we get
<br><br>${1 \over m}$ = 4
<br><br>$\Rightarrow$ m = ${1 \over 4}$
<br><br>For x<sup>2</sup>
= 2by line y = ${x \over 4}$ + 4 is tangent
<br><br>$\therefore$ x<sup>2</sup> = 2b$\left( {{x \over 4} + 4} \right)$
<br><br>$\Rightarrow$ x<sup>2</sup> - ${{bx} \over 2}$ - 8b = 0
<br><br>For tangent to the parabola Discriminant = 0
<br><br>$\Rightarrow$ ${{{b^2}} \over 4}$ + 32b = 0
<br><br>$\Rightarrow$ b = -128
About this question
Subject: Mathematics · Chapter: Conic Sections · Topic: Parabola
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