Question

The point $(5, - 7)$ lies outside the circle

• A. $x^2 + y^2 -8x = 0$
• B. $x^2 + y^2 - 5x + 7y = 0$
• C. $x^ 2 + y ^2 - 5x + 7y - 1 = 0$
• D. $x^2 + y^2 - 8x + 7y - 2 = 0$

Answer 1

Answer: (A)

$x^2 + y^2 -8x = 0$

Answer 2

The correct answer is A:$x^2+y^2-8x=0$
Given that;
The point is ;(5,-7) means we have to test options, f(a,b)=0⇤⇥on the circle
remember if, f(a,b)>0⇤⇥outside the circle
f(a,b)<0⇤⇥inside the circle
Option A:
$\therefore$ $f_1$(5,-7); $5^2+(-7)^2-8\times5=34>0$ (outside)
Option B:
$f_2(5,-7);5^2+(-7)^2-5\times5+7\times7=0$ (on the circle)
Option C:
$f_3(5,-7);5^2+(-7)^2-5\times5+7\times(-7)-1=-1<0$ (inside the circle)
Option D:
$f_4(5,-7);5^2+(-7)^2-8\times5+7\times(-7)-2=-17<0$ (inside the circle)
Hence, we can conclude option A is correct as per the question