Question

If a circle having the point (–1, 1) as its centre touches the straight line x + 2y + 9 = 0, then the co-ordinates of the point(s) of contact are -

• A. (–3, 3)
• B. (–3, –3)
• C. (0, 0)
• D. $\left( \frac { 7 } { 3 } , \frac { - 17 } { 3 } \right)$

Answer 1

Answer: (B)

(–3, –3)

Answer 2

̃ cp = r ̃ r = $\left| \frac { - 1 + 2 ( 1 ) + 9 } { \sqrt { 1 + 2 ^ { 2 } } } \right|$ = $\left( \frac { 10 } { \sqrt { 5 } } \right)$

\ Eq. of circle is ̃ (x + 1)² + (y – 1)² = 20 ...(2)

Now, check by opsitor P(x₁, y₁) = ?