Question

The point in the first quadrant of the ellipse x2/25+y2/144=1
at which the tangent makes equal
angles with the axes is​

Answer 1

Given : ellipse  x²/25  + y²/144 = 1  

To Find : the point in the first quadrant at which the tangent makes equal angles with the axes

a) ( 2,144/3)

b) (25/13,144/13)

c) (-25/13,144/13)

d) (-25/13,-144/13)​

Solution:

x²/25  + y²/144 = 1

=>  2x/25 + (2y/144) dy/dx = 0

=>  x/25  + (y/144) dy/dx = 0

=>  (y/144) dy/dx = -x/25

=> dy/dx =  - 144x/25y

tangent makes equal angles with the axes

and Quadrant is  1st

hence slope = - 1

=> - 1 =  - 144x/25y

=> 25y = 144x

=> y = 144x/25

x²/25  + y²/144 = 1

=> x²/25  + (144x/25)²/144 = 1

=> x²/25  + 144x²/25² = 1

=> 25x² + 144x² = 25²

=> 169x² = 25²

=>  x² = 25²/169

=> x² = 25²/13²

=> x  = 25/13  as 1st Quadrant

y = 144x/25  = 144/13

(25/13,144/13)  

option B is correct

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