Maths-
General
Easy

Question

If the equation fraction numerator x squared over denominator 9 minus k end fraction plus fraction numerator y squared over denominator 5 minus k end fraction equals 1 represents an ellipse then

  1. k straight I with not stretchy hat on top left square bracket 5 comma 9 right square bracket
  2. k straight I with not stretchy hat on top left parenthesis 5 comma 9 right parenthesis    
  3. k<5    
  4. k>5    

hintHint:

Compare the equation with the equation of hyperbola.

The correct answer is: k<5


    fraction numerator x squared over denominator 9 minus k end fraction plus fraction numerator y squared over denominator 5 minus k end fraction equals 1

T h i s space e q u a t i o n space r e p r e s e n t s space e q u a t i o n space o f space h y p e r b o l a space x squared over a squared plus y squared over b squared equals 1 space w h e r e space a comma b greater than 1

F r o m space b o t h space t h e space e q u a t i o n s comma space w e space c a n space g e t
9 minus k greater than 1 space a n d space 5 minus k greater than 1
minus open parentheses k minus 9 close parentheses greater than 1 space a n d space minus open parentheses k minus 5 close parentheses greater than 1
k minus 9 less than 1 space a n d space k minus 5 less than 1
k less than 9 space a n d space k less than 5

I f space w e space d r a w space i t space o n space t h e space n u m b e r space l i n e comma space w e space g e t space k less than 5 space a s space c o m m o n.

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