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Suppose that the foci of the ellipse {{{x}^{{2}}}}{{9}}+{{{y}^

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Suppose that the foci of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{5} = 1$ are $(f_{1}, 0) a n d (f_{2}, 0)$ where $f_{1} > 0 a n d f_{2} < 0 .$ Let $P_{1} a n d P_{2}$ be two parabolas with a common vertex at (0, 0) and with foci at $(f_{1} .0) a n d$ (2f_2 , 0), respectively. Let $T_{1}$ be a tangent to $P_{1}$ which passes through $(2 f_{2}, 0)$ and $T_{2}$ be a tangents 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 $(\frac{1}{m 1 2} + m 22)$ is

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Charlotte Discussed

Suppose that the foci of the ellipse

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

are

(f_{1}, 0) a n d (f_{2}, 0)

where

f_{1} > 0 a n d f_{2} < 0 .

Let

P_{1} a n d P_{2}

be two parabolas with a common vertex at (0, 0) and with foci at

(f_{1} .0) a n d

(2f_2 , 0), respectively. Let

T_{1}

be a tangent to

P_{1}

which passes through

(2 f_{2}, 0)

and

T_{2}

be a tangents 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 22)

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Question Text

Suppose that the foci of the ellipse

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

are

(f_{1}, 0) a n d (f_{2}, 0)

where

f_{1} > 0 a n d f_{2} < 0 .

Let

P_{1} a n d P_{2}

be two parabolas with a common vertex at (0, 0) and with foci at

(f_{1} .0) a n d

(2f_2 , 0), respectively. Let

T_{1}

be a tangent to

P_{1}

which passes through

(2 f_{2}, 0)

and

T_{2}

be a tangents 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 22)

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