NIMCET 2018 Question Paper with solutions

Question : 34 of 120

Marks: +1, -0

Through any point (x,y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve given that divides the rectangle formed by the two lines and the axes into two areas, one of the which is twice the other, represents a family of

circles
parabolas
hyperbolas
straight lines

Validate

Solution:

Area of rectangle = xy
Area of first part = 2 × Area of II nd part
∴

∫↖{x}↙{0}

ydx =

{2xy}/3

⇒ y =

2/3[y+x{dy}/{dx}]

⇒

y/3

{2x}/3{dy}/{dx}

⇒ y = 2x

{dy}/{dx}

⇒

{dx}/x

{2dy}/y

⇒ log x + log c = 2 log y
⇒ log cx = log

y^2

⇒

y^2

= cx
⇒ Which is a parabola

Go to Question:

Prev Question

Next Question