If A,B are the points of contact of the tangents drawn from the point P-2,-3 to the circle x^2+y^2-8x-10y+5=0 and the chord AB subtends an angle θ at…

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If A,B are the points of contact of the tangents drawn from the point P-2,-3 to the circle x^2+y^2-8x-10y+5=0 and the chord AB subtends an angle θ at P then tanθ=

MARKS Content Team · Accepted Answer

Correct answer: (B) 24/7. We have, x^2+y^2-8x-10y+5=0 ⇒x^2+y^2-8x-10y+16+25=16+25-5 ⇒x-4^2+y-5^2=6^2 Centre C≡4,5 Radius=CA=CB=6 units. Now, PA=PB=√S_1=√(4+9+16+30+5)=8 In ∆CAP, CA/PC=tan(θ)/2 ⇒tan(θ)/2=6/8=3/4 Now, tanθ=(2tanθ2)/(1-tan^2θ2)=64/(1-916) ⇒tanθ=64/716=24/7

If $A, B$ are the points of contact of the tangents drawn from the point $P (- 2, - 3)$ to the circle $x^{2} + y^{2} - 8 x - 10 y + 5 = 0$ and the chord $A B$ subtends an angle $θ$ at $P$ then $\tan θ =$

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Relevant Questions

If A,B are the points of contact of the tangents drawn from the point P-2,-3 to the circle x2+y2-8x-10y+5=0 and the chord AB subtends an angle θ at P then tanθ=

Solution

Relevant Questions

If $A, B$ are the points of contact of the tangents drawn from the point $P (- 2, - 3)$ to the circle $x^{2} + y^{2} - 8 x - 10 y + 5 = 0$ and the chord $A B$ subtends an angle $θ$ at $P$ then $\tan θ =$