Question:
A variable circle passes through the point <span class="math-inline">\(A(a, b)\)</span> & touches the x-axis. Show that the locus of the other end of the diameter through A is <span class="math-inline">\((x - a)^{2} = 4by\)</span>.
True
False
Depends on A
None of the above
Step-by-Step Solution
Key Concept: General
Since chord are perpendicular, therefore if one makes an angle θ then the other will make an angle (90° - θ) with x-axis.
Correct Answer: (r₁r₂)^(4/3) = 16a²(r₁^(2/3) + r₂^(2/3))