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The Cartesian equation of the sides BC,C...

The Cartesian equation of the sides BC,CA, AB of a triangle are respectively `u_(1)=a_(1)x+b_(1)y+c_(1)=0, u_(2)=a_(2)x+b_(2)y+c_(2)=0` and `u_(3)=a_(3)x+b_(3)y+c_(3)=0`. Show that the equation of the straight line through A bisectig the side `bar(BC)` is `(u_(3))/(a_(3)b_(1)-a_(1)b_(3))=(u_(2))/(a_(1)b_(2)-a_(2)b_(1))`

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The diagonals of the parallelogrma formed by the lines a_(1)x+b_(1)y+c_(1)=0,a_(1)x+b_(1)y+c_(1)^(1)=0, a_(2)x+b_(2)y+c_(1)=0,a_(2)x+b_(2)+c_(1)^(1)= will be right angles if

If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

If |(1+a_(1),a_(2),a_(3)),(a_(1),1+a_(2),a_(3)),(a_(1),a_(2),1+a_(3))|=0 then a_(1)+a_(2)+a_(3)=

If the equation of the locus of a point equi-distant from the points (a_(1), b_(1)) and (a_(2),b_(2)) is (a_(1)-a_(2))x+(b_(1)-b_(2))y+c=0 then the value of c is

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If ax^(2) + by^(2) = 1, a_(1) x^(2) + b_(1)y^(2) = 1 , then show that the condition for orthogonality of above curves is (1)/(a)-(1)/(b)=(1)/(a_(1))-(1)/(b_(1))

AAKASH SERIES-STRAIGHT LINES-EXERCISE 3.4( LONG ANSWER QUESTIONS)
  1. If p and q are the lengths of the perpendiculars from the origin to th...

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  2. Find the equations of the line passing through the point of intersecti...

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  3. A variable straight line drawn through the point of intersection of th...

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  4. Two adjacent sides of a parallelogram are given by 4x+5y=0, 7x+2y=0 an...

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  5. Find the orthocentre of the triangle whose vertices are (5,-2),(-1,2),...

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  6. Find the orthocentre of the triangle whose vertices are (-5,-7),(13,2)...

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  7. Find the orthocentre of the triangle formed by 4x-7y+10=0, x+y-5=0, 7x...

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  8. Find the orthocentre of the triangle whose sides are 7x+y-10=0, x-2y+5...

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  9. Find the orthocentre of the triangle formed by the lines 2x-y=2,3x-2...

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  10. Find the circumcenter of the triangle whose vertices are (-2,3) , (2 ,...

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  11. Find the circumcentre of the triangle whose vertices are (1,3) (0,-2) ...

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  12. Find the circumcentre of the triangle whose vertices are (1,3) (-3,5) ...

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  13. Find the circumcentre of the triangle whose sides are given by x+y=0, ...

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  14. Find the circumcentre of the triangle whose sides are given by x+y=0, ...

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  15. Find the incentre of the triangle formed by the straight lines x=1,y=1...

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  16. Find the incentre of the triangle formed by the straight lines x+1=0,3...

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  17. Area of the triangle formed by the lines 2x-y-5=0, x-5y+11=0, x+y-1=0 ...

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  18. The Cartesian equation of the sides BC,CA, AB of a triangle are respec...

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