Question
For what value of k, the line 2y – x + k = 0 touches the parabola x2 + 4y = 0-
- 2
- –1/2
- –2
- ½
Hint:
solve the two equations for obtaining the quadratic equation and then solve it.
The correct answer is: –1/2
k=-1/2
2y-x+k = 0
Y= x/2-k/2
Substituting the value of y in the parabola, we get
x2 + 4(x/2-k/2)=0
since the line touches the curve, D=0
this gives us 4+ 8k=0
k=-1/2
when a quadratic equation has 2 equal roots, the D value is 0 . D= b^2 - 4ac.=0
this gives us the possible value(s) of k
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