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Rectangular Hyperbola

If three dist...

Question

If three distinct normals can be drawn to the parabola $y^{2} - 2 y = 4 x - 9$ from the point (2a, b), then the least integral value of a is ___.

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Solution

The given parabola is $(y - 1)^{2} = 4 (x - 2)$
Vertex $\equiv$ (2, 1) Focus (3, 1)
$∴ 2 a > 4 \Rightarrow a > 2$

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