If A = [( x , y ): x 2 + y 2 = 25 ] And B = [( x , y ): x 2 + 9 y 2 = 144 ] , then A ∩ B contains Options: A . &nbsp One point B . &nbsp Three points C . &nbsp Two points D . &nbsp Four points

Answer: Option D : D A = Set of all values (x,y) : x 2 + y 2 = 25 = 5 2 B = x 2 144 + y 2 16 = 1 i.e., x 2 ( 12 ) 2 + y 2 ( 4 ) 2 = 1 Clearly , A ∩ B consists of four points.

If A = [(x,y): x2+y2=25] And B = [(x,y): x2+9y2=144], then A∩B contains

Question

If A = [( $x, y$ ): $x^{2} + y^{2} = 25$ ] And B = [( $x, y$ ): $x^{2} + 9 y^{2} = 144],$ then $A \cap B$ contains

Options:

A . One point

B . Three points

C . Two points

D . Four points

Answer: Option D
:
D

A = Set of all values (x,y) : $x^{2} + y^{2} = 25 = 5^{2}$

B = $\frac{x^{2}}{144} + \frac{y^{2}}{16} = 1$ i.e., $\frac{x^{2}}{(12)^{2}} + \frac{y^{2}}{(4)^{2}} = 1$

Clearly , $A \cap B$ consists of four points.

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