JEE Main 2022 Mathematics question
Let the function − x, x > 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola at a point P on it passes through the point (8a, 8a − 1) but does not pass through the point (−1/a, 0). If the equation of the normal at P is , then is equal to .
Answer: 45
Solution
− 1)/x, so f decreases in (0, 1/2) and increases in (1/2, ), giving a = 1/2. The parabola is and the point is (4, 3). A tangent y = mx + 1/(2m) through (4, 3): 3 = 4m + 1/(2m), so m = 1/2 or m = 1/4. The tangent y = x/2 + 1
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