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Maths-

General

Easy

Question

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

(1, 0)
(−1, 0)
(0, 1)
(0, −1)

The correct answer is: (−1, 0)

See Fig. 13.66. The equation of the tangent at $open parentheses x subscript 1 end subscript comma y subscript 1 end subscript close parentheses$ on the parabola $y to the power of 2 end exponent equals 4 a x text is end text$
$y y subscript 1 end subscript equals 2 a open parentheses x plus x subscript 1 end subscript close parentheses$
Therefore, in this case, a = 1. The coordinates at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text are end text L left parenthesis 12 right parenthesis$
$L subscript 1 end subscript left parenthesis 1 comma negative 2 right parenthesis text . The equation of tangent at end text L text and end text L subscript 1 end subscript text are end text 2 y equals 2 left parenthesis x plus 1 right parenthesis$
$text and end text minus 2 y equals 2 left parenthesis x plus 1 right parenthesis comma text which gives end text x equals negative 1 comma y equals 0 text . Thus, the end text$
$text required point of intersection is end text left parenthesis negative 10 right parenthesis text . end text$

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