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Prove that the product of the perpendicu...

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))`

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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+bbeta^2)/(sqrt((a-b)^2+4h^2))

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

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

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 is b^2

Prove that the product of the perpendiculars from the foci upon any tangent to the ellipse x^2/a^2+y^2/b^2=1 is b^2

Prove that the product of the perpendicular from the foci on any tangent to the ellips (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is equal to b^(2)

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

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2),0) and (-sqrt(a^2-b^2),0) to the line x/a costheta + y/b sintheta=1 is b^2 .

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2),0) and (-sqrt(a^2-b^2),0) to the line x/a costheta + y/b sintheta=1 is b^2 .

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
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  2. The distance of a point (x1, y1) from two straight lines which pass th...

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  3. Prove that the product of the perpendiculars from (alpha,beta) to the ...

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  4. Find the area enclosed by the graph of x^2y^2-9x^2-25 y^2+225=0.

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

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  6. Show that the equation of the pair of lines bisecting the angles be...

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

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  8. Through a point A on the x-axis, a straight line is drawn parallel to ...

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

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

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

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

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  13. If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the ...

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

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  15. If the lines px^2-qxy-y^2=0 makes the angles alpha and beta with X-axi...

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  16. Find the joint equation of the pair of lines which pass through the ...

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  17. 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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  18. The distance between the two lines represented by the equation 9x^2-24...

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  19. If the gradient one of the lines ax^2+2h x y+by^2=0 is twice that of t...

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  20. If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the a...

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