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Maths-

General

Easy

Question

Angle between the tangents to the curve $y equals x to the power of 2 end exponent minus 5 x plus 6$ at the point (2, 0) and (3, 0) is

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

The correct answer is: $fraction numerator pi over denominator 2 end fraction$

Since, $y equals x to the power of 2 end exponent minus 5 x plus 6$
$therefore blank fraction numerator d y over denominator d x end fraction equals 2 x minus 5$

Now, $m subscript 1 end subscript equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript open parentheses 2 comma blank 0 close parentheses end subscript equals 4 minus 5 equals negative 1$

And $m subscript 2 end subscript equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript open parentheses 3 comma blank 0 close parentheses end subscript equals 6 minus 5 equals 1$

Now, $m subscript 1 end subscript m subscript 2 end subscript equals negative 1 cross times 1 equals negative 1$

Hence, angle between the tangents is $fraction numerator pi over denominator 2 end fraction$

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