If the line 2 x -3 y = k touches the parabola y ²=6 x , then find the value of k

Step-by-step solution

aligned Given x= 3 y+k 2 & . . and y²=6 x & y²=6 ( 3 y+k 2 ) y²=3(3 y+k) y²-9 y-3 k=0 & . . aligned If line (1) touches parabola (2) then roots of quadratic equation ( 3 ) is equal (-9)²=4 1 (-3 k) k=-27 / 4