Question bank/JEE Main/Mathematics

Variable ellipses are drawn with x = -4 as a directrix and
origin as corresponding foci. The locus of extremities of minor axes of
these ellipses is
pj nh?kZo`Ùk cuk;s tkrs gSa ftu x = -4 gS,oa laxr ukfHk ewy
fcUnq gS rks nh?kZo`Ùk y?kqv{k

Ay^2 = 4xBy^2 = 2xCy^2 = xDx^2 = 4y

Show answer and solution▾

[IMAGE] Now vc k = b and h = ae
Also lkFk gh $\frac{e}{a}$ - ae = 4 $\Rightarrow$ a(1 - e^2) = 4e
$\Rightarrow$ a^2 (1 - e^2) = 4ae
$\Rightarrow$ b^2 = 4h
$\Rightarrow$ k^2 = 4h $\Rightarrow$ $\boxed{y^{2} = 4x}$

Source: Grass-G / M-27 Mathematics Paper 2 15 Jan.docx