Let α be the angle which a tangent to the parabola y2=4ax makes with its axis, the distance between the tangent and a parallel normal will be

Question

Let α be the angle which a tangent to the parabola y2=4ax makes with its axis, the distance between the tangent and a parallel normal will be (A) asin2α cos2α  (B) acosecα sec2α  (C) atan2α  (D) acos2α

Tardigrade Admin · Accepted Answer

Tangent of parabola y2=4ax is y=mx+(a/m) .......(.i.) Where m=tanα And equation of normal parallel to eq. (.i.) is y=mx-2am-am3 ....(.ii.) Distance between eq. (.i.) and (.ii.) is (|(a/m) + 2 a m + a m3|/√(1 + m2)) =(a (1 + m2)2/m √(1 + m2))=(a (1 + m2)3 / 2/m)=(a (1 + (tan)2 α )3 / 2/tan α )=(a (sec)3 α /tan α ) =asec2α cosecα

Q. Let $α$ be the angle which a tangent to the parabola $y^{2} = 4 a x$ makes with its axis, the distance between the tangent and a parallel normal will be

$a s i n^{2} α co s^{2} α$

$a cosec α se c^{2} α$

$a t a n^{2} α$

$a co s^{2} α$

Q. Let α be the angle which a tangent to the parabola y2=4ax makes with its axis, the distance between the tangent and a parallel normal will be

asin2αcos2α

acosecαsec2α

atan2α

acos2α

Q. Let $α$ be the angle which a tangent to the parabola $y^{2} = 4 a x$ makes with its axis, the distance between the tangent and a parallel normal will be

$a s i n^{2} α co s^{2} α$

$a cosec α se c^{2} α$

$a t a n^{2} α$

$a co s^{2} α$