Question

Equation of the tangent to the circle, at the point $(1,-1)$, whose centre is the point of intersection of the straight lines $x-y=1$ and $2x+y=3$ is:

• A. $x+4y+3=0$
• B. $3x-y-4=0$
• C. $x-3y-4=0$
• D. $4x+y-3=0$

Answer 1

The correct option is A $x+4y+3=0$

Point of intersection of lines

$x-y=1$ and $2x+y=3$

$is$ $(\frac{4}{3},\frac{1}{3})$

Slope of $OP=\frac{\frac{1}{3}+1}{\frac{4}{3}-1}=\frac{\frac{4}{3}}{\frac{1}{3}}=4$

Slope of tangent $=-\frac{1}{4}$

Equation of tangent $y+1=-\frac{1}{4}(x-1)$

$\Rightarrow 4y+4=-x+1$

$\Rightarrow x+4y+3=0$