Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaMiscellaneous/MixedMedium2 min

MathematicsMediumsingle choice

If $2 p^{2} - 3 q^{2} + 4 pq - p = 0$ and a variable line $p x + q y = 1$ always touches a parabola whose axis is parallel to X -axis, then equation of the parabola is

Options:

Answer:

Solution:

The parabola be $(y - a)^{2} = 4 b (x - c)$

Equation of tangent is $(y - a) = - \frac{p}{q} (x - c) - \frac{b q}{p}$

Comparing with $px + qy = 1$ , we get $cp^{2} - bq^{2} + apq - p = 0$

$∴ \frac{c}{2} = \frac{b}{3} = \frac{a}{4} = 1 \Rightarrow$ the equation is $(y - 4)^{2} = 12 (x - 2)$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Miscellaneous/Mixed

⏱ 2m

Doubts & Discussion

Loading discussions...