Math miscellaneousMedium
Question
If C is centre and A and B are two points on conic 4x2 - 9y2 - 8x - 36y + 4 = 0 such that ∠ ACB = 
, then CA-2 + CB-2 is equal to -
, then CA-2 + CB-2 is equal to -Options
A.
B.
C.
D.
Solution
9(y + 2)2 - 4(x - 1)2 = 36
CA is inclined to x-axis at an angle θ then
= (1 + CA cos θ, - 2 + CA sin θ)
B = (1 - CB sin θ, - 2 + CB sin θ)
9CA2 sin2θ - 4CA2 cos2θ = 36
9CB2 cos2θ - 4CB2 sin2θ = 36
add 36(CA-2 + CB-2) = 5
CA-2 + CB-2 =
CA is inclined to x-axis at an angle θ then
= (1 + CA cos θ, - 2 + CA sin θ)
B = (1 - CB sin θ, - 2 + CB sin θ)
9CA2 sin2θ - 4CA2 cos2θ = 36
9CB2 cos2θ - 4CB2 sin2θ = 36
add 36(CA-2 + CB-2) = 5
CA-2 + CB-2 =
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