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If the line y = mx - (m-1) cuts the circ...

If the line `y = mx - (m-1)` cuts the circle `x^2+y^2=4` at two real and distinct points then total values of m are

A

`m in (1, 2)`

B

`m=1`

C

`m=2`

D

`m in R`

Text Solution

Verified by Experts

The correct Answer is:
D
If the line `y= mx-(m-1)` cuts the circle in two distinct points, then
Length of the perpendicular from the centre `lt` Radius.
`rArr |(mxx0-0-(m-1))/(sqrt(m^(2)+1))| lt 2`
`rArr (|m-1|)/(sqrt(m^(2)+1))lt2`
`rArr (m-1)^(2)lt 2(m^(2)+1)`
`rArr m^(2)+2m+1 gt 0`
`rArr (m+1)^(2)gt0`, which is true for all `m in R`.
Hence, option (d) is correct.
`ul("ALITER")` The equation of the line is `y-1=m(-1)`.
Clearly, it passes through (1, 1) which is an interior point of the circle. So, the line cuts the circle for all values of m.
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OBJECTIVE RD SHARMA ENGLISH-CIRCLES-Chapter Test
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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 a circle passing through (0,0), (1,0) and touching the C...

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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 is of le...

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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 the line y=x by the circle x^(2)+y^(2)-2x=0 is AB. 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. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

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

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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 2 sqrt(2) whose centre lies on th...

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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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