Question

If the length of the chord made on the circle
by its secant x + y + 2 = 0) is 6 and centre
of the circle is (2, 4) then the equation of
the circle is​

Answer 1

Answer:

you have to solve

length of chord made on the circle

x+y=2+6

=8-0=8 cm

then the equation of circle is 8 cm

Answer 2

The length of perpendicular from (2,4) on the line x+y+2=0 would be

$\frac{2 + 4 + 2}{ \sqrt{2} } = \frac{8}{ \sqrt{2} } = 4 \sqrt{2}$

The perpendicular from the centre onto a chord bisects it.

So, the base of the triangle so formed would be 3.

The radius being the hypotenuse of the right angled triangle

$Radius = \sqrt{ {3}^{2} + (4 \sqrt{ {2} } {)}^{2}} = \sqrt{9 + 32} = \sqrt{41}$