Question

Equation of tangent to the circle $x^2+y^2-6x-4y+5=0$ which make an angle of ${45}^o$ with $x-$axis is

• A. $y=x+7$
• B. $y=x+4$
• C. $y=x+3$
• D. $y=-x+3$

Answer 1

Answer: (D)

$y=-x+3$

Let the equation be $y=x+c$

$⟹y-x-c=0$

Equation of circle is $(x-3{)}^2+(y-2{)}^2=8$

So, using condition for tangent, we get

$|\frac{3-2-c}{{\sqrt{1}}^2+1^2}|=$Radius$=2\sqrt{2}$

$⟹|1-c|=4$

$⟹1-c=\pm 4$

So, $c=-3$ or $c=5$

So line will be either $y=x-3$ or $y=x+5$