Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaMiscellaneous/MixedMedium2 min

MathematicsMediumsingle choice

If the parabola $y = (a - b) x^{2} + (b - c) x + (c - a)$ touches the $x$ -axis then the line $a x + b y + c = 0$

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Solution:

Solving equation of parabola with x -axis $(y = 0)$

We get $(a - b) x^{2} + (b - c) x + (c - a) = 0$ , which should have two equal values of x ,

as $x$ -axis touches the parabola $\Rightarrow (b - c)^{2} - 4 (a - b) (c - a) = 0$ $\Rightarrow (b + c - 2 a)^{2} = 0 \Rightarrow - 2 a + b + c = 0 \Rightarrow a x + b y + c = 0$ always passes through $(- 2, 1)$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Miscellaneous/Mixed

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