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The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is:

(A) An ellipse

(B) A parabola

(C) A circle

(D) A rectangular hyperbola

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is an Objective Type Questions as classified in NCERT Exemplar

    Sol:

    Since,  the  slope  of  the    to  the  curve  =x:y∴              dydx=xy      ⇒ydy=xdxIntegrating  both  sides,  we  have         ∫ydy=∫xdx⇒                y22=x22+c    ⇒y2=x2+2c⇒       y2−x2=2c=k  which  is  rectangular  hyperbola.Hence,  the  correct  option  is  (d).

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