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The product of the perpendiculars from o...

The product of the perpendiculars from origin to the pair of lines `a x^2+2h x y+b y^2 + 2gx + 2fy + c =0` is

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Prove that the product of the perpendiculars from (alpha,beta) to the pair of lines a x^2+2h x y+b y^2=0 is (aalpha^2+2halphabeta+b beta^2)/(sqrt((a-b)^2+4h^2))

Prove that the product of the perpendiculars from (alpha,beta) to the pair of lines a x^2+2h x y+b y^2=0 is (aalpha^2+2halphabeta+b beta^2)/(sqrt((a-b)^2+4h^2))

Prove that the product of the perpendiculars from (alpha,beta) to the pair of lines a x^2+2h x y+b y^2=0 is (aalpha^2-2halphabeta+bbeta^2)/(sqrt((a-b)^2+4h^2))

The product of the perpendiculars drawn from the point (1,2) to the pair of lines x^(2)+4xy+y^(2)=0 is

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

The equation to the pair of lines perpendicular to the pair of lines 3x^(2)-4xy+y^(2)=0 , is

A point moves so that the distance between the foot of perpendiculars from it on the lines a x^2+2hx y+b y^2=0 is a constant 2d . Show that the equation to its locus is (x^2+y^2)(h^2-a b)=d^2{(a-b)^2+4h^2}dot

The locus of the foot of the perpendicular drawn from the origin to any chord of the circle x^(2)+y^(2)+2gx+2fy+c=0 which substents a right angle at the origin is

Statement I . The equation 2x^2-3xy-2y^2+5x-5y+3=0 represents a pair of perpendicular straight lines. Statement II A pair of lines given by ax^2+2hxy+by^2+2gx+2fy+c=0 are perpendicular if a+b=0

Show that the equation of the pair of lines bisecting the angles between the pair of bisectors of the angles between the pair of lines a x^2+2h x y+b y^2=0 is (a-b)(x^2-y^2)+4h x y=0.

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Find the area enclosed by the graph of x^2y^2-9x^2-25 y^2+225=0

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  2. Show that the pairs of straight lines 2x^2+6x y+y^2=0 and 4x^2+18 x y+...

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  3. The product of the perpendiculars from origin to the pair of lines a x...

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  4. Find the angle between the straight lines joining the origin to the ...

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  5. Through a point A(2,0) on the x-axis, a straight line is drawn paralle...

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  6. Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

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  7. Does equation x^2+2y^2-2sqrt(3)x-4y+5=0 satisfies the condition a b c+...

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  8. Find the value of lambda if 2x^2+7x y+3y^2+8x+14 y+lambda=0 represents...

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  9. Find the distance between the pair of parallel lines x^2+4x y+4y^2+3x+...

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  10. If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y...

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  11. Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0 u...

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  12. If the component lines whose combined equation is px^(2)-qxy-y^(2)=0 m...

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  13. Find the joint equation of pair of lines which passes through origin a...

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  14. If the sum of the slopes of the lines given by x^2-2c x y-7y^2=0 is fo...

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  15. The distance between the two lines represented by the  sides of an equ...

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  16. If the gradient one of the lines x^2+h x y+2y^2=0 is twice that of the...

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  17. If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is a bisector of th...

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  18. Two pairs of straight lines have the equations y^(2)+xy-12x^(2)=0andax...

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  19. If the equation of the pair of straight lines passing through the poin...

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  20. If one of the lines given by the equation 2x^(2)+pxy+3y^(2)=0 coincide...

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