QJEEM21Maf353: JEE Main 2021 Mathematics - Class 11 JEEM21Maf353 Solution: If a line along a chord of the circle 4x 2 + 4y 2 + 120x + 675…

Question

Verified Solution • 2025–26 Session moderate

If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point (

-

30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :

Accepted Answer

Equation of tangent to y² = 30 x

y = mx +

{{30} \over {4m}}

Pass thru (

-

30, 0) : a =

-

30m +

{{30} \over {4m}}

\Rightarrow

m² = 1/4

\Rightarrow

m =

{1 \over 2}

or m =

-

{1 \over 2}

At m =

{1 \over 2}

: y =

{x \over 2}

+ 15

\Rightarrow

x

-

2y + 30 = 0

l_AB = 2

\sqrt {{R^2} - {P^2}}

= 2

\sqrt {{{225} \over 4} - {{225} \over 5}}

\Rightarrow

l_AB = 30 .

\sqrt {{1 \over {20}}}

=

{{{15} \over {\sqrt 5 }}}

= 3

{\sqrt 5 }

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