The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is


Correct option is

y2 = –12(x – 3)

Let P(x, y) be the point for which we have to find the locus.

Writed1 = OP = {(– 0)2 + (y – 0)2}1/2 

d2 = distance of P from 

Given d1 + d2 = 4, d12 = (6 – x)  y2 + x2

                      = (6 – x)2 d1 = 4 – d2  

              y2 = –12(x – 3)



The normal at an end of a latus rectum of the ellipse  passes through an end of the minor axis if


If an ellipse slides between two perpendicular straight line, then the locus of its center is   


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The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse. x2 + 9y2 = 9, meets the auxillary circle at the point M, then the area of the triangle with vertices at A, M and the origin is


The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.


Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 – 5xy + 6y2) = 0 represents


The pints of intersection of the two ellipse x2 + 2y2 – 6x – 12y + 23 = 0 and 4x2 + 2y2 – 20x – 12y + 35 = 0.


The tangent at any point P of the hyperbola  makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then


The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y2 = 8x, is 


The length of the subnormal to the parabola y2 = 4ax at any point is equal to