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prove that the product of the perpendicu...

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)|`

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PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
  1. If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of para...

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  2. If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pa...

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  3. prove that the product of the perpendiculars drawn from the point (x1,...

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  4. The orthocentre of a triangle whose vertices are (0,0),(sqrt3,0) and (...

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  5. The image of the point (3,8) with respect to the line x+3y=7 is

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  6. The equations of the lines representing the sides of a triangle are 3x...

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  7. The point (4,1) undergoes the following three transformations successi...

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  8. A is (a,0) and B is (-a,0). If P is a point such that anglePAB - angle...

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  9. The points (-a,-b).(0,0),(a,b) and (a^2, ab) are

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  10. The medians AD and BE of a triangle ABC with vertices A(0, b), B(0, 0)...

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  11. The vertices of a rhombus taken in order are (2,-1), (3,4), (-2,3), th...

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  12. The coordinates of the point P on the lines 2x+3y+1=0, such that |PA-P...

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  13. One vertex of the equilateral triangle with centroid at the origin and...

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  14. If t1, t2 and t3 are distinct, the points (t1, 2at1+at1^3), (t2,2at2+a...

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  15. If (-6,-4), (3,5),(-2,1) are the vertices of a parallelogram, then rem...

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  16. A line passing through the point P(4,2) meets the x and y-axis at A an...

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  17. If P-=(1,0), Q-=(-1, 0), R-=(2,0) are three given points, then the loc...

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  18. A straight line segment AB of length 'a' moves with its ends on the ax...

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  19. Let A be any variable point on the X-axis and B the point (2,3). The p...

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  20. Let AB be a line segment of length 4 unit with the point A on the line...

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