Question

The angle between $x^2+y^2-2x-2y+1=0$ and line $y=\lambda x+1-\lambda$ is

• A. $0^o$
• B. ${45}^o$
• C. ${30}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

$y=\lambda x+1-\lambda \cdot$
$(y-1)=\lambda (x-1)$
This line passes through a fixed point $(1,1)$ which is centre of circle $x^2+y^2-2x-2y+1=0\cdot$
angle beth $x^2+y^2-2x-2y+120=0$ and $y=\lambda x+1-\lambda$ is ${90}^{\circ }$
$y=\lambda x+1-\lambda$ is normal to circle.