Circles
Circle
nta_abhyas_2025
Grade 11
Question:
The chord nearest to the centre of the circle will be the longest chord. From options, the given lines are at distances $\frac{2}{3}, \frac{3}{5}, \frac{2}{3}, \frac{7}{5}$ respectively from the centre $(3,4)$.
Step-by-Step Solution
Key Concept: For a fixed circle, the longest chord closest to the centre is the diameter; among other chords, the chord closest to the centre is the longest.
To find which line gives the longest chord, we need the line closest to the centre. Computing distances from $(3,4)$ to each given line using the distance formula $d = \frac{|ax_0 + by_0 + c|}{\sqrt{a^2+b^2}}$, we find that option (A) gives the minimum distance, hence the longest chord.
Correct Answer: 1