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Maths-

General

Easy

Question

The angle between the tangents to the curve $y to the power of 2 end exponent equals 2 a x$ at the point where $x equals fraction numerator a over denominator 2 end fraction$ , is

$\frac{π}{6}$
$π / 4$
$\frac{π}{3}$
$π / 2$

The correct answer is: $pi divided by 2$

We have,
$y to the power of 2 end exponent equals 2 a x$ …(i)

$rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator a over denominator y end fraction$

Putting $x equals fraction numerator a over denominator 2 end fraction$ in (i), we get $y equals plus-or-minus a$

Thus, the two points on the curve (i) are $P open parentheses a divided by 2 comma blank a close parentheses$ and $Q open parentheses a divided by 2 comma blank minus a close parentheses$

$therefore open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript P end subscript equals 1 blank a n d blank open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript Q end subscript equals negative 1$

Clearly, $open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript P end subscript cross times open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript Q end subscript equals negative 1$

Hence, the angle between the tangents at $P$ and $Q$ is a right angle

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