Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaChordsMedium2 minQB

MathematicsMediumsingle choice

If the line $y - 3 x + 3 = 0$ cuts the parabola $y^{2} = x + 2$ at A and B , then PA. PB is equal to (where $P \equiv (3, 0)$ )

Answer:

Solution:

$y - 3 x + 3 = 0$ can be rewritten as

$\frac{y - 0}{\frac{3}{2}} = \frac{x - 3}{\frac{1}{2}} = r$

Solving (1) with the parabola $y^{2} = x + 2$

$\frac{3 r ^{2}}{4} - \frac{r}{2} - 3 - 2 = 0 \Rightarrow P A . PB = r_{1} r_{2} = \frac{4 ( 3 + 2 )}{3}$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Chords

⏱ 2mℹ️ Source: QB

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