If $\theta $ denotes the acute angle between the curves, $y = 10 - {x^2}\,{\rm{ and}}\,{\rm{ }}y = 2 + {x^2}$ at a point of their intersection, then $\left| {\tan \theta } \right|$ is equal to

JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Medium

1 of 1

Analyzing +4 | -1

\theta

denotes the acute angle between the curves,

y = 10 - {x^2}\,\mathrm{ and}\,\mathrm{ }y = 2 + {x^2}

at a point of their intersection, then

\left| {\tan \theta } \right|

is equal to

View answer and explanation

Correct option: B

\frac{8}{{15}}

Option B (8/15) is correct because it is the absolute value of the tangent of the acute angle between the two curves at their intersection points, calculated using their derivatives.

More Questions from STRAIGHT LINES

Practice All Chapter MCQs →

If the three lines

x-3 y=p, a x+2 y=q

and

a x+y=r

form a right-angled triangle then :
The orthocentre of the triangle whose vertices are

\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

is
The distance between the parallel lines

y = 2\;x + 4

and

6x = 3y + 5

is The distance between the pair of lines given by

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

is Find the image of the point

(3,8)

with respect of the line

x+3 y=7

assuming the line to be plane mirror: The centroid of the triangle whose three sides are given by the combined equation

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0