The room was silent. A boy behind him started hyperventilating. Arjun closed his eyes. He saw the grey Cengage cover. He remembered a similar problem from Parabola – Exercise 3, Multiple Correct, Question 17. He recalled the trick: the tangent at (at², 2at) for y²=4ax. Here a=3. t = y/(2a) = -6/(6) = -1. Tangent: y*(-1) = x + 3*(-1)² → -y = x+3 → x+y+3=0. Directrix: x = -3. Intersect P: (-3,0). Focus: (3,0). Distance = 6.
Arjun pointed at the coaching modules. "They are too easy. The exam is different."
He marked the answer in 90 seconds. It felt like breathing.
His father picked up the Cengage Algebra book. It was heavy, the spine barely cracked. "Son," he said, "A sword is not a sword because it shines. It is a sword because it has been sharpened against stone. This book is your stone. Stop worshipping it. Start cutting yourself on it."
In his next coaching mock test, a question appeared: "From point P(2, 3), tangents are drawn to the circle x² + y² = 8. Find the angle between the tangents."
Default: Small
Small 1
Small 2
Medium
Medium 1
Medium 2
Large
Large 1
Large 2
Large 3