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If the circle x^2+y^2-4x-8y-5=0 intersec...

If the circle `x^2+y^2-4x-8y-5=0` intersects the line `3x-4y=m` at two distinct points, then find the values of `m`.

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To solve the problem, we need to find the values of \( m \) such that the circle given by the equation \( x^2 + y^2 - 4x - 8y - 5 = 0 \) intersects the line \( 3x - 4y = m \) at two distinct points. ### Step 1: Rewrite the Circle Equation We start with the circle's equation: \[ x^2 + y^2 - 4x - 8y - 5 = 0 \] We can rewrite this in standard form by completing the square. ...
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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at t...

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  2. An infinite number of tangents can be drawn from (1,2) to the circle x...

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  3. If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two dis...

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  4. The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . ...

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  5. Find the equation of the circle which cuts the three circles x^2+y^2-3...

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  6. Find the equations to the common tangents of the circles x^2+y^2-2x-6y...

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  7. Equation of the smaller circle that touches the circle x^2+y^2=1 and p...

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  8. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

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  9. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

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  10. The equation of three circles are given x^2+y^2=1,x^2+y^2-8x+15=0,x^2+...

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  11. If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2...

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  12. A circle passes through the origin and has its center on y=x If it cut...

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

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  14. The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle ...

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  15. If S(1)=alpha^(2)+beta^(2)-a^(2), then angle between the tangents from...

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  16. If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1...

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  17. Find the angle between the two tangents from the origin to the circle ...

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  18. Two circles C1 and C2 intersect at two distinct points PandQ in a line...

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  19. Find the equation of the tangent at the endpoints of the diameter of ...

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  20. Find the equations of the tangents to the circle x^2+y^2-6x+4y=12 whic...

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