A straight line L1:x−2y+10=0 meets the circle with equation x2+y2=100 at B in the first quadrant. If another line L2 through B is perpendicular to L1 cuts y-axis at P(0,t), then the value of t is
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Solution
From the given conditions, we know
Line L1:x−2y+10=0 Perpendicular line to L1 is 2x+y+λ=0⋯(1) Now, as ∠B is 90∘ so L2 must pass through (10,0) 20+0+λ=0⇒λ=−20 Now, 2x+y−20=0⇒0+t−20=0∴t=20