Circles
Chords of a Circle
Grade 11
Question:
<p>If two chords of the circle \(x^2 + y^2 - ax - by = 0\), drawn from the point \((a, b)\) is divided by the x-axis in the ratio 2:1 then:</p>
<p>(a) \(a^2 > 3b^2\)</p>
<p>(b) \(a^2 < 3b^2\)</p>
<p>(c) \(a^2 > 4b^2\)</p>
<p>(d) \(a^2 < 4b^2\)</p>
Step-by-Step Solution
Key Concept: Use the section formula for points dividing chords and substitute into the circle equation to find the constraint.
<p>Let the chords from \((a,b)\) intersect the x-axis at points that divide the chords in ratio 2:1. Using the section formula and the condition that these points lie on the circle, we can establish a relationship between a and b. Through coordinate geometry and the constraint that the point \((a,b)\) lies on the circle, we derive that \(a^2 > 3b^2\).</p>
Correct Answer: A