If \((a, b)\) is a point on the chord \(A B\) of the circle, where the ends of the chord are \(A=(-2,3)\) and \(B \equiv(3,2)\) then : (a) \(a \in[-3,2], b \in[2,3]\) (b) \(a \in[2,3], b \in[-3,2]\) (c) \(a \in[-2,2], b \in[-3,3]\) (d) \(a \in[-3,3], b \in[-2,2]\)

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The solution is: (a) \(a \in[-2,3], b \in[2,3]\)

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TABLE OF CONTENTS :

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Step 1 Understanding the Problem

Read the problem carefully. We are given the end points of a chord in a circle as \(A=(-2,3)\) and \(B \equiv(3,2)\). We need to find the range within which the points \((a, b)\) on the chord \(AB\) will vary. This requires understanding of coordinate geometry and chord properties.

Step 2 Plotting the Points

Plot the points \(A\) and \(B\) given in the problem. We can see that \(A\) is situated on the left side (negative x-coordinates) and \(B\) is on the right (positive x-coordinates). Also, the y-coordinate of \(A\) is greater than \(B\). Hence, a point on the chord will vary in such a way to satisfy the properties of chords in a circle and also should lie in between \(A\) and \(B\).

Step 3 Finding the Range

The x-coordinate of any point on the chord will be in between -2 and 3 i.e \(a \in[-2,3]\) as per the points \(A\) and \(B\). Similar logic applies for the y-coordinate. \(B\)'s y-coordinate is 2 and \(A\)'s y-coordinate is 3, so any point \(b\) on the chord will have y-coordinate varying from 2 to 3 i.e \(b \in [2,3]\). Hence, the point \((a, b)\) will be such that the x-coordinate of \(a\) is in between -2 and 3 and the y-coordinate of \(b\) is in between 2 and 3.

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Chapter 1: Chapter 1

If \((a, b)\) is a point on the chord \(A B\) of the circle, where the ends of the chord are \(A=(-2,3)\) and \(B \equiv(3,2)\) then : (a) \(a \in[-3,2], b \in[2,3]\) (b) \(a \in[2,3], b \in[-3,2]\) (c) \(a \in[-2,2], b \in[-3,3]\) (d) \(a \in[-3,3], b \in[-2,2]\)

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Step 1 Understanding the Problem

Step 2 Plotting the Points

Step 3 Finding the Range

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More chapters from the book ‘Skills in Mathematics for All Engineering Entrance Examinations: Coordinate Geometry’

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