The locus of vertices of family of parabolas, y = a x 2 + 2 a 2 x + 1 is ( a  = 0 ) a curve passing through

y ⇒ a y − ( 1 − a 3 ) ∴ V er t e x ( α , β ) ⇒ β ⇒ C u r v e i sy = a x 2 + 2 a 2 x + 1 = ( x + a ) 2 = ( − a , 1 − a 3 ) = 1 + α 3 = 1 + x 3

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Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaGeneralEasy2 minQB

MathematicsEasysingle choice

The locus of vertices of family of parabolas, $y = a x^{2} + 2 a^{2} x + 1$ is $(a \neq = 0)$ a curve passing through

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Solution:

$y \Rightarrow \frac{y - ( 1 - a ^{3} )}{a} ∴ V er t e x (α, β) \Rightarrow β \Rightarrow C u r v e i sy = a x^{2} + 2 a^{2} x + 1 = (x + a)^{2} = (- a, 1 - a^{3}) = 1 + α^{3} = 1 + x^{3}$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:General

⏱ 2mℹ️ Source: QB

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