Consider two circles C_1:x^2+y^2=25 and C_2:(x-α)^2+y^2=16, where α∈(5,9). Let the angle between the two radii (one to each circle) drawn from one of…

Question

Consider two circles C_1:x^2+y^2=25 and C_2:(x-α)^2+y^2=16, where α∈(5,9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C_1and C_2 be sin^(-1)√638. If the length of common chord of C_1 and C_2 is β, then the value of (αβ)^2 equals _________.

MARKS Content Team · Accepted Answer

Correct answer: 1575. Given, C_1:x^2+y^2=25, C_2:(x-α)^2+y^2=16 and 5<α<9 Now, plotting the diagram we get, Also, given sinθ=√638 Now, from the above diagram, finding the area of ΔOAP we get, ΔOAP=1/2×α(β)/2=1/2×5×4sinθ ⇒αβ=40×√638 ⇒αβ=5×√63 ⇒(αβ)^2=25×63=1575

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Consider two circles C1:x2+y2=25 and C2:(x-α)2+y2=16, where α∈(5,9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C1and C2 be sin-1638. If the length of common chord of C1 and C2 is β, then the value of (αβ)2 equals _________.

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