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If S(1)=alpha^(2)+beta^(2)-a^(2), then a...

If `S_(1)=alpha^(2)+beta^(2)-a^(2)`, then angle between the tangents from `(alpha, beta)` to the circle `x^(2)+y^(2)=a^(2)`, is

A

`tan^(-1)((a)/(sqrt(S_(1))))`

B

`2tan^(-1)((a)/(sqrt(S_(1))))`

C

`2 tan^(-1)((sqrt(S_(1)))/(a))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let PT and PT' be the tangents drawn from `P(alpha, beta)` to the circle `x^(2)+y^(2)=a^(2)`, and let `angleTPT'=theta.` If O is the centre of the circle, then
`angleTPO=angleT'PO=theta//2`
`:. tan. (theta)/(2)=(OT)/(OP)=(a)/(sqrt(S_(1)))rArr theta = 2 tan^(-1)((a)/(sqrt(S_(1)))`
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OBJECTIVE RD SHARMA-CIRCLES-Chapter Test
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  3. The two circles x^(2)+y^(2)-2x-2y-7=0 and 3(x^(2)+y^(2))-8x+29y=0

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  4. The centre of the circle passing through (0, 0) and (1, 0) and touchin...

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  5. The circle x^2+y^2=4 cuts the circle x^2+y^2+2x+3y-5=0 in A and B, The...

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  6. One of the limit point of the coaxial system of circles containing x^(...

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  7. A circle touches y-axis at (0, 2) and has an intercept of 4 units on t...

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  8. The equation of the circle whose one diameter is PQ, where the ordinat...

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  9. The circle x^2 + y^2+ 4x-7y + 12 = 0 cuts an intercept on y-axis equal...

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  10. Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0...

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  11. The angle between the pair of tangents from the point (1, 1/2) to the...

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  12. The intercept on line y = x by circle x^2 + y^2- 2x = 0 is AB. Find eq...

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  13. If 3x+y=0 is a tangent to a circle whose center is (2,-1) , then find ...

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  14. Locus of the middle points of chords of the circle x^2 + y^2 = 16 whic...

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  15. Two tangents to the circle x^2 +y^2=4 at the points A and B meet at P(...

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  16. A tangent is drawn to the circle 2(x^(2)+y^(2))-3x+4y=0 and it touch...

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  17. the length of the chord of the circle x^(2)+y^(2)=25 passing through ...

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  18. If the points A(2, 5) and B are symmetrical about the tangent to the c...

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  19. The equation of the circle of radius 2sqrt(2) whose centre lies on the...

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  20. Prove that the maximum number of points with rational coordinates on a...

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  21. The equation of a circle C is x^(2)+y^(2)-6x-8y-11=0. The number of re...

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