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If the straight lines a^(2)x+ay+k=0, b^(...

If the straight lines `a^(2)x+ay+k=0, b^(2) x+by+k=0 and c^(2)x+cy+k=0 ( k ne 0)` are concurrent, show that at least two of the three constant a,b,c are equal.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. The equations of two equal sides AB and AC of an isosceles triangle AB...

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  2. One diagonal of a square is the portion of the straight line 7x+5y=35 ...

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  3. If the straight lines a^(2)x+ay+k=0, b^(2) x+by+k=0 and c^(2)x+cy+k=0 ...

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  4. Show that the circle x^(2)+y^(2)-2y-15=0 lies completely within the ci...

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  5. Two sides of a rhombus ABCD are parallel to the lines x-y=5 and 6x-y=3...

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  6. Two sides of a rhombus lyin in the first quadrant are given by 3x-4y=0...

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  7. A line joining two points A (2,0) and B(3,1) is rotated about A in the...

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  8. A (3,0) and B(6,0) are two fixed points and P(x(1),y(1)) is a variable...

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  9. Find the coordinates of the centroid of the triangle, formed by the li...

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  10. The points (1,3) and (5,1) are two oppsite vertices of a rectangle. Th...

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  11. Show that the lines ax+by+c=0, ax-by+c=0, ax-by=c ax+ by-c=0 (a ne b) ...

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  12. Let A(ct(1), (c)/(t(1))), B(ct(2),(c)/(t(2))) and C(ct(3),(c)/(t(3))) ...

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  13. The circle A and B of a line segment of constant length c unit slides ...

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  14. A variable striaght line of slope 4 intresects the hyprbola xy=1 at tw...

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  15. If x cos alpha+ y sin alpha=p, where p=(-sin^(2) alpha)/(cos alpha) be...

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  16. A tangent drawn from the point (4,0) to the circle x^(2)+y^(2)=8 touch...

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  17. A(x(1) y(1)) and B(x(2), y(2)) are two given points on a circle. If th...

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  18. If 4a^(2)-5b^(2)+6a+1=0 find the equation of the circle for which the...

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  19. Find the point of the circle x^(2)+y^(2)-6x+4y=0 which is (i) nearest ...

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  20. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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