Parabola
Parabola
nta_pyq_2025_jan
Grade 11
Question:
Let the parabola y = x + px - 3, meet the coordinate axes at the points P, Q and R . If the circle C with centre 2 at (-1, -1) passes through the points P , Q and R, then the area of △P QR is :
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
y = x 2 + px - 3 (3) Let P(\alpha, 0), Q(\beta, 0), R(0, -3) Circle with centre (-1, -1) is (x + 1) + (y + 1) = r 2 2 2 Passes through (0, -3) 2 2 2 1 + (-2) = r ] 2 r = 5 2 2 (x + 1) + (y + 1) = 5 Put y = 0 2 (x + 1) = 5 - 1 2 (x + 1) = 4 x + 1 = $\pm$2 x = 1 or x = -3 \therefore P (1, 0) and Q(-3, 0) ∣ 1 0 1∣ Area of △PQR = 1 ∣ 2 ∣ -3 0 1 ∣ ∣ = 6 ∣ 0 -3 1∣
Correct Answer: 3