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Focii of Ellipse

Suppose that ...

Question

Suppose that the foci of the ellipse are (f₁, 0) and (f₂, 0) where f₁ >0 and f₂ <0 .Let P₁ and P₂ be two parabolas with a common vertex at (0, 0) and with foci at (f₁, 0) and (2f₂, 0), respectively. Let T₁ be a tangent to P₁ which passes through (2f₂, 0) and T₂ be a tangent to P₂ which passes through (f₁, 0). If m₁ is the slope of T₁ and m₂ is the slope of T₂, then the value of is

A

$4$

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B

$2$

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C

$6$

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D

$8$

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Solution

The correct option is A
$4$

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Q. Suppose that the foci of the ellipse

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Q. Suppose that the foci of the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1

(f_{1}, 0)

(f_{2}, 0)

f_{1} > 0

f_{2} < 0

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P_{2}

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(2 f_{2}, 0)

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m_{1}

is the slope of

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m_{2}

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then the value of

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Suppose that the foci of the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ are $(f_{1}, 0)$ and $(f_{2}, 0)$ where $f_{1} > 0$ and $f_{2} < 0$ . Let $P_{1}$ and $P_{2}$ be two parabolas with a common vertex at $(0, 0)$ and with foci at $(f_{1}, 0)$ and $(2 f_{2}, 0)$ respectively. Let $T_{1}$ be a tangent to $P_{1}$ which passes through $(2 f_{2}, 0)$ and $T_{2}$ be a tangent to $P_{2}$ which passes through $(f_{1}, 0)$ . If $m_{1}$ is the slope of $T_{1}$ and $m_{2}$ is the slope of $T_{2}$ , then the value of $(\frac{1}{m_{1}^{2}} + m_{2}^{2})$ is

In $R^{3}$ , consider the planes $P_{1} : y = 0$ and $P_{2} : x + z = 1$ . Let $P_{3}$ be a plane , different from $P_{1}$ and $P_{2}$ , which passes through the intersection of $P_{1}$ and $P_{2}$ . If the distance of the point (0, 1, 0) from
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