Which of the following equations of a line intercepts on the circle x2+y2-6x-8y=0 a chord of longest length?

Question

Which of the following equations of a line intercepts on the circle x2+y2-6x-8y=0 a chord of longest length? (A) y-x=0 (B) x+y=0 (C) x+y=2 (D) 3x+4y-2=0

Tardigrade Admin · Accepted Answer

The chord nearest to the centre of the circle will be the longest chord.
From options, we see that the given lines are at a distance of

\frac{1}{2}, \frac{7}{2}, \frac{5}{2}, \frac{23}{5}

respectively from the centre

(3, 4)

.
Hence,

(A)

is correct

Q. Which of the following equations of a line intercepts on the circle $x^{2} + y^{2} - 6 x - 8 y = 0$ a chord of longest length?

$y - x = 0$

$x + y = 0$

$x + y = 2$

$3 x + 4 y - 2 = 0$

The chord nearest to the centre of the circle will be the longest chord.
From options, we see that the given lines are at a distance of $\frac{1}{2}, \frac{7}{2}, \frac{5}{2}, \frac{23}{5}$ respectively from the centre $(3, 4)$ .
Hence, $(A)$ is correct

Q. Which of the following equations of a line intercepts on the circle x2+y2−6x−8y=0 a chord of longest length?

y−x=0

x+y=0

x+y=2

3x+4y−2=0