JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Analyzing +4 | -1

If the roots of the equation

a x^2+b x+10=0

are not real and distinct where

a, b \in R

and

\alpha

and

\beta

are the values of

a

and

b

for which

5 a+b

is minimum, then the family of lines

\alpha(4 x+2 y+3)+\beta(x-y-1)=0

are concurrent at

View answer and explanation

Correct option: C

(-1 / 6,-7 / 6)

Option C (

(-1 / 6,-7 / 6)

) is correct because it is the intersection point of the family of lines derived from the minimum value condition.

More Questions from STRAIGHT LINES

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

a x+y=r

\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\}

y = 2\;x + 4

6x = 3y + 5

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

(3,8)

x+3 y=7

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