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A point moves so that the sum of its dis...

A point moves so that the sum of its distances from `(a e ,0)a n d(-a e ,0)` is `2a ,` prove that the equation to its locus is `(x^2)/(a^2)+(y^2)/(b^2)=1` , where `b^2=a^2(1-e^2)dot`

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. A point moves so that the sum of its distances from (a e ,0)a n d(-a e...

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  2. If a vertex of a triangle is (1,1) , and the middle points of two side...

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  3. If two vertices of a parallelogram are (3,\ 2),\ (-1,\ 0) and the ...

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  4. If a triangle has it's orthocenter at (1,1) and circumcentre (3/2,3/4)...

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  5. One end of a thin straight elastic string is fixed at A(4,-1) and the ...

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  6. Find the centroid and incentre of the triangle whose vertices are (2, ...

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  7. If the vertices of a trianglehave integral coordinates, prove that the...

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  8. Show that the equation of the locus of a point which moves so that the...

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  9. A stick of length l slides with its ends on two mutually perpendicular...

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  10. if x and y coordinates of a point P in x-y plane are given by x=(ucosa...

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  11. A straight line L is perpendicular to the line 5x-y=1 . The area of th...

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  12. Find the equation of the line passing through the point (2,3) and maki...

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  13. The equation of the straight line through the point of intersection of...

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  14. Find the points on the line x+y=4 that lies at a unit distance from th...

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  15. A line is such that its segment between the lines 5x -y+4=0 and 3x +4y...

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  16. lines L1:ax+by+c=0 and L2:lx+my+n=0 intersect at the point P and make ...

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  17. The st. lines 3x + 4y =5 and 4x-3y = 15 interrect at a point A(3,-1)....

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  18. The equations of the perpendicular bisectors of the sides A Ba n dA C ...

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  19. If (h, r) is the foot of the perpendicular from (x1, y1) to lx+my+n=0,...

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  20. Equations of two straight lines are xcos alpha + ysin alpha = p and xc...

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  21. The side AB,BC,CD and DA of a quadrilateral are x+2y=3, x=1, x-3y=4, 5...

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