If 3 x+y+k=0 is a tangent to the circle x²+y²=10 , the values of k are

Step-by-step solution

Given, line is 3 x+y+k=0 y=-3 x-k And equation of circle is x²+y²=10 Here, a²=10, m=-3, c=-k If given line touches the circle, then length of intercept =0 2 a² (1+m² )-c² 1+m² =0 2 10(1+9)-k² 1+9 =0 100-k² =0 100-k²=0 k= 10 Alternative : If the given line is tangent to the circle, then the length of the perpendicular from the centre upon the line is equal to the radius of the circle. aligned & i.e. | a x₁+b y₁+c a²+b² |=r & | 3 0+6 0+k (3)²+(1)² |= 10 & | k 10 |= 10 & k= 100 k= 10 aligned