Question

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

• A. One point
• B. Three points
• C. Two points
• D. Four points

Answer 1

Answer: (D)

Four points

Answer 2

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 ∩ B consists of four points.