Statement 1 : If `aa n db` are real numbers and `c >0,` then the locus represented by the equation `|a y-b x|=csqrt((x-a)^2+(y-b)^2)` is an ellipse. Statement 2 : An ellipse is the locus of a point which moves in a plane such that the ratio of its distances from a fixed point (i.e., focus) to that from the fixed line (i.e., directrix) is constant and less than 1.

Find the equation of the locus of a point which moves such that the ratio of its distances from (2,0)a n d(1,3) is 5: 4.

Find the locus of a point , which moves such that its distance from the point (0,-1) is twice its distance from the line 3x+4y+1=0

The locus of point which moves in such a way that its distance from the line (x)/(1)=(y)/(1)=(z)/(-1) is twice the distance from the plane x+y+z=0 is

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (!=1) . Then, identify the locus of the point.

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (!=1) . Then, identify the locus of the point.

Find the equation of the locus of a point whose distance from the y-axis is equal to its distance from (2,1,-1).

A point P(x,y) moves so that the sum of its distances from point (4,2) and (-2,2) is 8. If the locus of P is an ellipse then its length of semi-major axis is

Let C_1 and C_2 be two circles with C_2 lying inside C_1 . A circle C lying inside C_1 touches C_1 internally and C_2 externally. Statement : 1 Locus of centre of C is an ellipse. Statement (2) The locus of the point which moves such that the sum of its distances from two fixed points is a constant greater than the distance between the two fixed points is an ellipse. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

A point P(x, y) moves so that the sum of its distances from the points S(4, 2) and S^(') (-2, 2) is 8. Find the equation of its locus and show that it is an ellipse.