A circle of radius 2 unit passes through the vertex and the focus of the parabola y^ 2 = 2x and touches the parabola y = (x - 1/4)^ 2 + , where > 0. Then (4 - 8)^ 2 is equal to _____.

JEE Main 2022 Mathematics question

A circle of radius 2 unit passes through the vertex and the focus of the parabola and touches the parabola , where . Then is equal to .

Answer: 63

Solution

The vertex is (0, 0) and the focus is (1/2, 0). The circle through them is x(x − 1/2) + , i.e. − x/2 + , with centre (1/4, ) and radius , so . The vertex of the parabola

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-034624