JEE MATHEMATICS MCQ: STRAIGHT LINES

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Application +4 | -1

Let a variable line passing through the centre of the circle

x^2+y^2-16 x-4 y=0

, meet the positive coordinate axes at the points

A

and

B

. Then the minimum value of

O A+O B

, where

O

is the origin, is equal to

View answer and explanation

Correct option: B

Option B (18) is correct because the minimum value of OA + OB is found by minimizing the function representing the sum of the intercepts.

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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