x ∝ y2 and y = 2a when x = a, then show that y2 = 4ax . ( WBBSE – 2019 )

x ∝ y²and y = 2a when x = a, then show that y² = 4ax .

Solution : x ∝ y²

⇒ x = ky² ——————-( 1 )

where k is variation constant .

when x = a and y 2a, then from equation ( 1 ),

a = k ( 2a )²

⇒ a = k × 4a²

⇒ 1 = k ( 4a )

⇒ k = 1 / ( 4a )

putting the value of k = 1 / ( 4a ) in equation ( 1 ), we get,

x = ky²

⇒ x = { 1 / ( 4a ) } y²

∴ y² = 4ax ( showed )