Let A and B be two distinct point on the parabola y2 = 4x. If the axis of the parabola touches the circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

Engineering

Mathematics

Standard Parabola

Question

Let A and B be two distinct point on the parabola y² = 4x. If the axis of the parabola touches the circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

$\frac{- 1}{r}$

$\frac{2}{r}$

$\frac{1}{r}$

$\frac{- 2}{r}$

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y-coordinates of the centre = radius = r

$∴$ t₁ + t₂ = r or – 2

$∴$ slopes of AB = $\frac{2}{t_{1} + t_{2}}$

$= \frac{2}{r} or \frac{- 2}{r}$