Question

A line L passing through the focus of the parabola y² = 4

(x – 1) intersects the parabola in two distinct points. If ‘m’ be the slope of the line L then-

• A. –1 < m < 1
• B. m < –1 or m > 1
• C. mÎ R
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let y = Y, x – 1 = X. Then the equation is
Y² = 4X.

So, the focus = (1, 0)_{X, Y} = (2, 0).

Any line through the focus is y = m(x – 2). Solving this with y² = 4(x – 1),

m² (x – 2)² = 4(x – 1) or m²x² – 4(m² + 1) x + 4(m² + 1) = 0.

If m ¹ 0, D = 16(m² + 1)² – 16m² (m² + 1) = 16(m² + 1) > 0 for all m.

But, if m = 0 then x does not have two real distinct values.

So m Î R except m = 0.