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Maths-

General

Easy

Question

For the parabola $y to the power of 2 end exponent equals 4 a x$ , the ratio of the subtangent to the abscissa is

1 : 1
2 : 1
$x : y$
$x^{2} : y$

The correct answer is: 2 : 1

We have,
$y to the power of 2 end exponent equals 4 a x rightwards double arrow 2 y blank fraction numerator d y over denominator d x end fraction equals 4 a rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator 2 a over denominator y end fraction$

$therefore$ Length of the subtangent $equals fraction numerator y over denominator fraction numerator d y over denominator d x end fraction end fraction equals fraction numerator y over denominator fraction numerator 2 a over denominator y end fraction end fraction equals fraction numerator y to the power of 2 end exponent over denominator 2 a end fraction equals fraction numerator 4 a x over denominator 2 a end fraction equals 2 x$

So, subtangent : Abscissa $equals 2 x blank colon x equals 2 blank colon 1$

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