Question

Find the pole of the line 3x+4y-12=0 with respect to the circle x^2+y^2=24​

Answer 1

Given:

The line 3x+4y-12=0 and the circle x^2+y^2=24​

To find:

Find the pole of the line 3x+4y-12=0 with respect to the circle x^2+y^2=24​

Solution:

From given, we have,

The pole of the line 3x+4y-12=0 and the circle x^2+y^2=24​

The pole of a line lx + my + n = 0 with respect to the circle x² + y² = a² is $(-\dfrac{la^2}{n}, -\dfrac{ma^2}{n})$

comparing the given equations with the standard equations, we get,

l = 3, m = 4, n = -12 and a² = 24

Thus we get,

$(-\dfrac{3 \times 24}{-12}, -\dfrac{4 \times 24}{-12})\\\\= (6, 8)$

Therefore, the pole of the line 3x+4y-12=0 with respect to the circle x^2+y^2=24​ is (6, 8)