Coordinate Geometry
Parabola, Tangents, Focus
jee_main_2026_april_4_shift_2
Grade 12
The tangent to the parabola y^2 = 8x at the point (2, 4) meets the x-axis at P. The distance from P to the focus of the parabola is:
Step-by-Step Solution
Key Concept: Find tangent equation, then x-intercept (P), then distance to focus (a, 0).
Step 1: y^2 = 8x => 4a = 8 => a = 2, focus = (2, 0). Step 2: Tangent at (2, 4): yy1 = 2a(x + x1) => 4y = 4(x + 2) => 4y = 4x + 8 => y = x + 2. Step 3: x-intercept: set y = 0 => x = -2, so P = (-2, 0). Step 4: Distance from P(-2, 0) to focus (2, 0) = 4.
Correct Answer: C