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Maths-

General

Easy

Question

If $A equals open curly brackets open parentheses x comma y close parentheses blank colon y equals fraction numerator 4 over denominator x end fraction comma x not equal to 0 close curly brackets$ and
$B equals open curly brackets open parentheses x comma y close parentheses colon x to the power of 2 end exponent plus y to the power of 2 end exponent equals 8 comma x comma y element of R close curly brackets$ , then

$A \cap B = ϕ$
$A \cap B$ contains one point only
$A \cap B$ contains two points only
$A \cap B$ contains 4 points only

The correct answer is: $A intersection B$ contains two points only

We have, $y equals fraction numerator 4 over denominator x end fraction$ and $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 8$
Solving these two equations, we have
$x to the power of 2 end exponent plus fraction numerator 16 over denominator x to the power of 2 end exponent end fraction equals 8 rightwards double arrow open parentheses x to the power of 2 end exponent minus 4 close parentheses equals 0 rightwards double arrow x equals plus-or-minus 2$
Substituting $x equals plus-or-minus 2$ in $y equals fraction numerator 4 over denominator x end fraction comma$ we get $y equals plus-or-minus 2$
Thus, the two curves intersect at two points only (2, 2) and $left parenthesis negative 2 comma blank 2 right parenthesis$ . Hence, $A intersection B$ contains just two points

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