Question

The mid-point of the chord $2x + y - 4 = 0$ of the parabola $y^2 = 4x$ is

• A. $\left( \frac{5}{2}, -1 \right)$
• B. $\left( -\frac{1}{2}, 1 \right)$
• C. $\left( \frac{3}{2}, -1 \right)$
• D. None of these

Hint:

To find the midpoint of a chord in a parabola, solve for the intersection points of the line and the parabola, then use the midpoint formula.

Answer 1

The Correct Option is A

To find the midpoint of the chord, we first find the equation of the chord and use the midpoint formula.
The equation of the chord is given by: \[ 2x + y - 4 = 0 \quad \text{and} \quad y^2 = 4x \] The intersection of this equation will give the points on the parabola.
Solving these equations, we find the midpoint to be $\left( \frac{5}{2}, -1 \right)$.