Question

If the line $y=7x-25$ meets the circle $x^2+y^2=25$ in the points A, B then the distance between A and B is

• A. $\sqrt{10}$
• B. $10$
• C. $5\sqrt{2}$
• D. $5$

Answer 1

Answer: (C)

The intersection point of line $y=7x-25$ and circle
$x^2+y^2=25$ is $x^2+{(7x-25)}^2=25$
$\Rightarrow$ $50x^2-350x+600=0$
$\Rightarrow$ $x^2-7x+12=0$
$\Rightarrow$ $(x-3)(x-4)=0$
$\Rightarrow$ $x=3,x=4$ and $y=-4,3$
$\therefore$ Coordinates of $A(3,-4)$ and $B(4,3)$
$\therefore$ Length, $AB=\sqrt{{(4-3)}^2+{(3+4)}^2}$
' $=\sqrt{1+49}=5\sqrt{2}$