Question

plz answer this question asap

Answer 1

Answer:  t = 20.

Line    L1:  x - 2 y + 10 = 0      ---(1)
                        =>  x = (2 y -10)   -- (2)

Circle  C:   x² + y² = 100      ---(3)

Substitute (2) in (3) to get coordinates of B.
              (2y-10)² + y² = 100
              5y² - 40 y + 100 = 100
               y = 0  or    y = 8.

Substitute in (1) to get:
                 x = (2y-10) =   -10  or   6

Point B is in 1st Quadrant.  =>  B = (6 , 8)

Slope of Line L1 given:   1/2. 
Slope of Line L2  ⊥ L1:    -1/(1/2) =  - 2

Line through B having a slope of -2 :     
       ( y - 8)/(x-6) = -2
         y + 2 x = 20    --- -(4)
        
This line cuts y - axis at (0, t).  Substitute the coordinates in (4).
     So:    t + 2 * 0 = 20
               t = 20.