The straight line y + x = 1 touches the parab | vedclass

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Question

(D) line touches a parabola if the quadratic equation formed by substituting the line equation into the parabola equation has a discriminant $D = 0$.F

Vedclass · Accepted Answer

all of the above

Vedclass · Answer

(D) line touches a parabola if the quadratic equation formed by substituting the line equation into the parabola equation has a discriminant $D = 0$.For $(A) x^2 + 4y = 0$:Substitute $y = 1 - x$:$x^2 + 4(1 - x) = 0 \Rightarrow x^2 - 4x + 4 = 0$.$D = (-4)^2 - 4(1)(4) = 16 - 16 = 0$. (Touches)For $(B) x^2 - x + y = 0$:Substitute $y = 1 - x$:$x^2 - x + 1 - x = 0 \Rightarrow x^2 - 2x + 1 = 0$.$D = (-2)^2 - 4(1)(1) = 4 - 4 = 0$. (Touches)For $(C) 4x^2 - 3x + y = 0$:Substitute $y = 1 - x$:$4x^2 - 3x + 1 - x = 0 \Rightarrow 4x^2 - 4x + 1 = 0$.$D = (-4)^2 - 4(4)(1) = 16 - 16 = 0$. (Touches)Since all options satisfy the condition,the correct answer is $(D)$.

The straight line $y + x = 1$ touches the parabola:

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