JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Hard

1 of 1

Analyzing +4 | -1

Let

m_1, m_2

be the slopes of two adjacent sides of a square of side a such that

a^2+11 a+3\left(m_1^2+m_2^2\right)

=220

. If one vertex of the square is

(10(\cos \alpha-

\sin \alpha), 10(\sin \alpha+\cos \alpha))

, where

\alpha \in\left(0, \frac{\pi}{2}\right)

and the equation of one diagonal is

(\cos \alpha-\sin \alpha) x

+(\sin \alpha+\cos \alpha) y=10

, then

72\left(\sin ^4 \alpha+\cos ^4 \alpha\right)

+a^2-3 a+13

is equal to :

View answer and explanation

Correct option: B

128

Option B (128) is the correct answer as it is obtained by calculating the side length and using the given equation to find the slopes, then substituting into the final expression.

More Questions from STRAIGHT LINES

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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