Question

Equation of tangent having slope as 1 to the circle $x^2+y^2=25$ is

• A. $x-y+5\sqrt{2}=0$
• B. $x-y-6\sqrt{2}=0$
• C. $x-y+6\sqrt{2}=0$
• D. $x-y-1+\sqrt{2}=0$

Answer 1

The correct option is A $x-y+5\sqrt{2}=0$

The equation of circle is $x^2+y^2=a^2$ and tangent is $y=mx+c$

$\Rightarrow$ $x^2+y^2=25$ and $m=1$ [ Given ]

From equation $a^2=25$

We know, $c^2=a^2(1+m^2)$

$\Rightarrow$ $c^2=25(1+1^2)$

$\Rightarrow$ $c^2=50$

$\therefore$ $c=5\sqrt{2}$

The equation of tangent is

$y=mx+c$

$\Rightarrow$ $y=\left(1\right)x+5\sqrt{2}$

$\therefore$ $x-y+5\sqrt{2}=0$