Question

The tangents at the extremities of each of two chords drawn from the point $(2,2)$ to the circle $x^2+y^2-2x-4y+1=0$ meet at points A and B, respectively. The equation of the line AB is

• A. $x=5$
• B. $x+y=4$
• C. $2x-y=2$
• D. $y=2$

Answer 1

The correct option is A $x=5$

Given circle, $x^2+y^2-2x-4y+1=0$

$(x-1{)}^2+(y-2{)}^2-1-4+1=0(x-1{)}^2+(y-2{)}^2=2^2$

Coordinates of $P(2,3)$

Slope of $PO=1$

Slope of $PA=(-1)$

Equation of $PA$

$(y-3)=-1(x-2)x+y=5$

Coordinates of $A(5,0)$

The tangent $PR$ and $QR$ meets at $A(5,0)$

The tangent $XY$ and $X^{\prime }{Y}^{\prime }$ meets at infinity $\left(B\right)$

Equation of line $AB$ is $x=5$