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Question: If m<sub>1</sub> and m<sub>2</sub> be the slopes of two perpendicular chord of equal length passing ...

If m1 and m2 be the slopes of two perpendicular chord of equal length passing through origin of circle

(x – 1)2 + (y + 2)2 = 5, then the value of is equal to–

A

809\frac { 80 } { 9 }

B

829\frac { 82 } { 9 }

C

839\frac { 83 } { 9 }

D

None of these

Answer

829\frac { 82 } { 9 }

Explanation

Solution

Let slope of OA = m

tan 450 = ∣m+21−2m∣\left| \frac { m + 2 } { 1 - 2 m } \right|

Ž |m + 2| = |1 – 2m|

Ž (m + 2) = (1 – 2m)

Ž m = 3 or – 13\frac { 1 } { 3 }

Ž = (m1 + m2)2 – 2m1m2

= 649+2=829\frac { 64 } { 9 } + 2 = \frac { 82 } { 9 }