Archive
17th of March 2017
Mathematics
Q:

At what point of the ellipse 16 x squared space plus space 9 y squared space space equals space 400 space does the ordinate decrease at the same rate at which the abscissa increases.

Ahuja8087 Ahuja - CBSE - Class XII Science

Friday, March 17, 2017 at 17:43:PM

A:

begin mathsize 12px style Given space that space the space ordinate space decreased space at space the space same space rate space at space which space the space abscissa space increases.
rightwards double arrow negative dy over dt equals plus dx over dt rightwards double arrow dy over dt equals negative dx over dt
Differentiating space wrt space 16 straight x squared plus 9 straight y squared equals 400 comma space we space get
32 straight x space dx over dt plus 18 straight y space dy over dt equals 0
rightwards double arrow 32 straight x space dx over dt plus 18 straight y space open parentheses negative dx over dt close parentheses equals 0
Simplifying comma space we space get
32 straight x minus 18 straight y equals 0 rightwards double arrow straight y space equals space fraction numerator 16 straight x over denominator straight y end fraction
Substitute space this space value space of space straight y space in space 16 straight x squared plus 9 straight y squared equals 400 space and space solve space for space straight x comma space
you space will space get space straight x equals plus-or-minus 3.
Then space evaluate space the space value space of space straight y space when space straight x equals 3 comma space and space when space straight x equals negative 3 comma space which space will space fetch space you space space the space required space points. end style

Friday, March 17, 2017 at 18:06:PM