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The line 3x-2y=k meets the circle x^(2)+...

The line `3x-2y=k` meets the circle `x^(2)+y^(2)=4r^(2)` at only one point, if `k^(2)=`

A

`20 r^(2)`

B

`52 r^(2)`

C

`(52)/(9) r^(2)`

D

`(20)/(9)r^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
The line `3x-2y-k=0` meets the circle `x^(2)+y^(2)=4r^(2)` at only one point. So, it is a tanget to the circle.
`:. |(3xx0-2xx0-k)/(sqrt(3^(2)+(-2)^(2)))|=2r rArr k^(2)=52r^(2)`
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OBJECTIVE RD SHARMA-CIRCLES-Chapter Test
  1. The line 3x-2y=k meets the circle x^(2)+y^(2)=4r^(2) at only one point...

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  2. The two circles x^2 + y^2 -2x+6y+6=0 and x^2 + y^2 - 5x + 6y + 15 = 0 ...

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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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