Exams Joint Entrance Examination Mathematics Straight Lines and Pair of Straight Lines Question 35 Question 35 of 303 Medium MCQ
Let A ( − 1 , 1 ) A(-1,1) A ( − 1 , 1 ) and B ( 2 , 3 ) B(2,3) B ( 2 , 3 ) be two points and P P P be a variable point above the line A B AB A B such that the area of \trianglePAB \trianglePAB \trianglePAB is 10. If the locus of P P P is a x + b y = 15 ax+by=15 a x + b y = 15 , then 5 a + 2 b 5a+2b 5 a + 2 b is :
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1 2 ∣ h k 1 − 1 1 1 2 3 1 ∣ = 10 − 2 x + 3 y = 25 − 6 5 x + 9 5 y = 15 \begin{gathered} \frac{1}{2}|\begin{array}{|c|}h \quad k \quad 1 \\ -1 \quad 1 \quad 1 \\ 2 \quad 3 \quad 1\end{array}|=10 \\ -2x+3y=25 \\ -\frac{6}{5}x+\frac{9}{5}y=15 \end{gathered} 2 1 ∣ h k 1 − 1 1 1 2 3 1 ∣ = 10 − 2 x + 3 y = 25 − 5 6 x + 5 9 y = 15
a = − 6 5 , b = 9 5 5 a = − 6 , 2 b = 18 5 \begin{gathered} a=-\frac{6}{5},b=\frac{9}{5} \\ 5a=-6,2b=\frac{18}{5} \end{gathered} a = − 5 6 , b = 5 9 5 a = − 6 , 2 b = 5 18
∴ \therefore ∴ 5 a + 2 b 5a+2b 5 a + 2 b = − 12 5 -\frac{12}{5} − 5 12 Answer the question to unlock