Question

The length of the common chord of the circle x^2+y^2-6x-16=0 and x^2+y^2-8x-9=0 is

Answer 1

Answer:

To find common chord simply subtract both equation.

$- 6x - 16 + 8x + 9 = 0 \\ 2x + 7 = 0$

Center of first circle is (-3 , 0 ) and radius

√(9+16) = 5

Perpendicular distance of 2x+7 = 0 from (-3, 0)

$p = \frac{2( - 3) + 7}{ \sqrt{ {2}^{2} } } = \frac{1}{2}$

Now use Pythagoras for h

$h = \sqrt{ {r}^{2} - {p}^{2} } = \sqrt{25 - \frac{1}{4} } \approx4.98$

So length will be

$2h \approx9.96$