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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 drawn from the point (x_1, y_1) to the pair of straight lines ax^2+2hxy+by^2=0 is |(ax_1^2+2hx_1y_1+by_1^2)/sqrt((a-b)^2+4h^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

If the perpendicular distance from origin to the straight line 4x-3y+P=0 is 2 unit,then the value of P is

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.

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

If the line (x/a)+(y/b)=1 moves in such a way that (1/(a^2))+(1/(b^2))=(1/(c^2)) , where c is a constant, prove that the foot of the perpendicular from the origin on the straight line describes the circle x^2+y^2=c^2dot

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 cos theta + y/b sin theta = 1 " is " b^(2) .

Through a point A (2,0) on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines a x^2+2h x y+b y^2=0 at B and Cdot If A B=B C , then (a) h^2=4a b (b) 8h^2=9a b (c) 9h^2=8a b (d) 4h^2=a b

Through a point A on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines a x^2+2h x y+b y^2=0 at B and Cdot If A B=B C , then (a) h^2=4a b (b) 8h^2=9a b (c) 9h^2=8a b (d) 4h^2=a b

Find the area of an equilateral triangle inscribed in the circle x^2 + y^2 + 2gx + 2fy + c = 0

CENGAGE PUBLICATION-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 po...

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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 equation of two straigh lines whose combined equation is 6x^(...

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

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  8. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

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  9. Find the distance between the pair of parallel lines x^(2)+4xy+4...

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

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  11. Find the equation of two straigh lines whose combined equation is 6x^(...

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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)-2cxy-7y^(2)=0 is...

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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 of one of the lines x^(2)+hxy+2y^(2)=0 twice that of ...

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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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