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The sides of a triangle have the combine...

The sides of a triangle have the combined equation `x^2-3y^2-2x y+8y-4=0` . The third side, which is variable, always passes through the point `(-5,-1)` . Find the range of values of the slope of the third line such that the origin is an interior point of the triangle.

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CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. The equations of two equal sides A Ba n dA C of an isosceles triangle ...

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  2. Find the area of the triangle formed by the line x+y=3 and the angle b...

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  3. The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=...

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  4. The equation of the lines passing through the point (1,0) and at a dis...

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  5. The number of values of k for which the lines (k+1)x+8y=4k and kx+(k+3...

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  6. For all real values of aa n db , lines (2a+b)x+(a+3b)y+(b-3a)=0 and m ...

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  7. The line x=c cuts the triangle with corners (0,0),(1,1) and (9,1) into...

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  8. The absolute value of the sum of the abscissas of all the points on th...

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  9. The point (x , y) lies on the line 2x+3y=6. The smallest value of the ...

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  10. The equations of the perpendicular bisectors of the sides A Ba n dA C ...

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  11. One of the diagonals of a square is the portion of the line x/2+y/3=2 ...

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  12. Two sides of a triangle are along the coordinate axes and the medians ...

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  13. The graph of y^2+2x y+40|x|=400 divides the plane into regions. Then ...

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  14. In a triangle A B C ,A=(alpha,beta)B=(2,3),a n dC=(1,3)dot Point A l...

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  15. If the straight lines 2x+3y-1=0,x+2y-1=0,and a x+b y-1=0 form a trian...

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  16. Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such...

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  17. If the area of the rhombus enclosed by the lines l x+-m y+-n=0 is 2 s...

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  18. In a triangle A B C , the bisectors of angles Ba n dC lies along the...

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  19. If a/(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family ...

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  20. P(m , n) (where m , n are natural numbers) is any point in the interio...

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