JEE MATHEMATICS MCQ: STRAIGHT LINES

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Application +4 | -1

The condition that the pair of straight line joining the origin to the intersections of the line

y=m x+c

and the circle

x^2+y^2=a^2

is at the right angles, is 

View answer and explanation

Correct option: B

2 c^2=a^2\left(1+m^2\right)

Option B (

2 c^2=a^2(1+m^2)

) is correct because it represents the condition for the pair of straight lines joining the origin to the intersection of the given line and circle to be at right angles.

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