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Slope Point Form of a Line

If three norm...

Question

If three normals can be drawn from $(h, 2)$ to the parabola $y^{2} = - 4 x$ , then

h < - 2

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h > 2

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2 < h < 2

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h is any real number

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Solution

The correct option is A $h < - 2$
If three normals can be drawn from $(h, 2)$ to parabola $y^{2} = - 4 x$
If $y^{2} = - 4 a x$ has three normals from $(h, k)$
Then $h < - 2 a$ (property)
Here $a = 1$
$h < - 2$

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Similar questions

(h, k)

2 (x - 1)^{2} + 2 (y - 1)^{2} = (x + y + 2)^{2}

If point (h, k) lies on the axis of the parabola $y^{2} = 4 a x$ , then find the condition for point (h, k) sothat exactly three normal can be drawn.

(h, k)

2 (x - 1)^{2} + 2 (y - 1)^{2} = (x + y + 2)^{2}

A O, A A_{1}, A A_{2}

y^{2} = 8 x

A (h, 0)

O A_{1} A_{2}

h

(4, 0)

y^{2} = 4 x

y^{2} = 4 a x, (a > 0)

(k, 0)

k > 2 a

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