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Parabola question

2015 · Shift 2 · Q31

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PYQ Library
JEE Advanced
Mathematics
Parabola
2015 · Shift 2 · Q31

Parabola question

2015 · Shift 2 · Q31

JEE AdvancedMathematicsParabolaNumerical+4 / −1

Suppose that the foci of the ellipse

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

are

\left( {{f_1},0} \right)

and

\left( {{f_2},0} \right)

where

{{f_1} \gt 0}

and

{{f_2} \lt 0}

. Let

{P_1}

and

{P_2}

be two parabolas with a common vertex at

(0,0)

and with foci at

\left( {{f_1},0} \right)

and

\left( 2{{f_2},0} \right)

, respectively. Let

{T_1}

be a tangent to

{P_1}

which passes through

\left( 2{{f_2},0} \right)

and

{T_2}

be a tangent to

{P_2}

which passes through

\left( {{f_1},0} \right)

. If

{m_1}

is the slope of

{T_1}

and

{m_2}

is the slope of

{T_2}

, then the value of

\left( {{1 \over {m_1^2}} + m_2^2} \right)

is

Numerical answer

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