If locus of image of a point (λ, 3), \lambda \in R in the line mirror 3x – 4y = 0 touches the circles of radius 3 units whose centre are (xi , yi) where i = 1, 2 and where 4xi + 3yi = 25 then find the value of \frac{1}{2} \left(\right. x_{1} + x_{2} + y_{1} + y

Engineering

Mathematics

Family of Circle

Question

If locus of image of a point (λ, 3), $λ \in R$ in the line mirror 3x – 4y = 0 touches the circles of radius 3 units whose centre are (x_i , y_i) where i = 1, 2 and where 4x_i + 3y_i = 25 then find the value of $\frac{1}{2} (x_{1} + x_{2} + y_{1} + y_{2}) .$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

From the figure, it is clear that

$\frac{x_{1} + x_{2}}{2} = 4, \frac{y_{1} + y_{2}}{2} = 3$

$∴ (\frac{x_{1} + x_{2} + y_{1} + y_{2}}{2}) = 7$ .