The coordinates of a point P on the line x + y + 13 = 0 , nearest to the circle x 2 + y 2 + 4 x + 6 y - 5 = 0 , are

Step-by-step solution

The distance of the centre - 2 , - 3 from the line x + y + 13 = 0 is - 2 - 3 + 13 2 = 4 2 units which is greater than the radius 3 2 Therefore, the line is neither tangent nor secant to the circle Hence, nearest point P on the line from the circle is the foot of the perpendicular from the centre on the line. ⇒ If P = h , k , then h + 2 1 = k + 3 1 = - - 2 - 3 + 13 2 ⇒ h = - 6 & k = - 7 ⇒ P = - 6 , - 7