Question
Question: If the straight line x+y = k touches the parabola y = x-x<sup>2</sup>, then k =...
If the straight line x+y = k touches the parabola y = x-x2, then k =
A
0
B
-1
C
1
D
2
Answer
1
Explanation
Solution
Eliminate y by using given equations.
⇒ k – x = x – x2
⇒ x2 – 2x + k =0
Since the given line is a tangent to the parabola, the above quadratic equation will have equal roots.
⇒ ∆ = 0 ⇒ 4 – 4k = 0 ⇒ k = 1