The equation of the line which is tangent to both the circle x²+y²=5 and the parabola y²=40 x is

Step-by-step solution

Let the equation of line by y=m x+C Since, this is the tangent to the circle x²+y²=5 So, aligned C &= a 1+m² &= 5 1+m² ...(i) aligned Also, the above line is tangent to the parabola y²=40 x So, c= a m = 10 m ...(ii) By Eqs. (i) and (ii), we get aligned 10 m &= 5 1+m² m⁴+m²-20 &=0 (m²+5 ) (m²-4 ) &=0 m² &=4 (m² -5 ) m &= 2 c= 5 Here, y &= 2 x 5 aligned