Question:

If A={(x,y):x2+y2=25}A = \{(x, y) : x^2 + y^2 = 25\} and B={(x,y):x2+16y2=144}B = \{(x, y) : x^2 + 16y^2 = 144\} then A∩BA \cap B contains

Updated On: Jul 6, 2022
  • one point
  • two points
  • three points
  • four points
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The Correct Option is D

Solution and Explanation

Given x2+16y2=144x^2 + 16y^2 = 144 ⇒x2122+y232=1\Rightarrow \frac{x^{2}}{12^{2}}+\frac{y^{2}}{3^{2}} = 1 (An ellipse whose major axis is xx-axis) …(A)\quad\ldots\left(A\right) and x2+y2=25x^{2} + y^{2} = 25 (a circle with radius r=5r = 5 units) …(B)\quad \ldots\left(B\right)
From the graph of AA and BB, we note that A∩BA \cap B have four points.
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Notes on Sets

Concepts Used:

Sets

Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.

Example of set: Set of vowels A={a,e,i,o,u}

Representation of Sets

There are three basic notation or representation of sets are as follows:

Statement Form: The statement representation describes a statement to show what are the elements of a set.

  • For example, Set A is the list of the first five odd numbers.

Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.

  • For example represent the set of vowels in roster form.

A={a,e,i,o,u}

Set Builder Form: 

  1. The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
  2. The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
  3. For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
  4. Sometimes a ":" is used in the place of the "|".