Question

The equations of any tangents to the circle

$x ^ { 2 } + y ^ { 2 } - 2 x + 4 y - 4 = 0$ is

• A. $y = m ( x - 1 ) + 3 \sqrt { 1 + m ^ { 2 } } - 2$
• B. $y = m x + 3 \sqrt { 1 + m ^ { 2 } }$
• C. $y = m x + 3 \sqrt { 1 + m ^ { 2 } } - 2$
• D. None of these

Answer 1

Answer: (A)

$y = m ( x - 1 ) + 3 \sqrt { 1 + m ^ { 2 } } - 2$

Answer 2

Equation of circle is $( x - 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 3 ^ { 2 }$ .

As any tangent to $x ^ { 2 } + y ^ { 2 } = 3 ^ { 2 }$ is given by

$y = m x + 3 \sqrt { 1 + m ^ { 2 } }$

Any tangent to the given circle will be

$y + 2 = m ( x - 1 ) + 3 \sqrt { 1 + m ^ { 2 } }$ $\Rightarrow y = m ( x - 1 ) + 3 \sqrt { 1 + m ^ { 2 } } - 2$