JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Application +4 | -1

(i) Find the integral values of '

h

' for which

h x^2-5 x y+4 {hy}^2+{x}+2 {y}-2=0

represents two real straight lines.
(ii) If the pair of lines represented by equation

k(k-3) x^2+16 x y+(k+1) y^2=0

are perpendicular to each other, then find

k

View answer and explanation

Correct option: A

{h}=1;{k}=1

Option A (h=1; k=1) is correct because the integral value of h is found using the determinant condition for a pair of lines, and k is found by setting the sum of the coefficients of x² and y² to zero for perpendicular lines.

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