Q. 45.0( 1 Vote )

# Find the locus of a point such that the sum of its distances from (0, 2) and (0, -2) is 6.

Answer :

**Key points to solve the problem:**

• **Idea of distance formula-** Distance between two points A(x_{1},y_{1}) and B(x_{2},y_{2}) is given by- **AB =**

**How to approach:** To find the locus of a point we first assume the coordinate of the point to be (h, k) and write a mathematical equation as per the conditions mentioned in the question and finally replace (h, k) with (x, y) to get the locus of the point.

**Let the point whose locus is to be determined to be (h,k)**

Distance of (h,k) from (0,2) =

Distance of (h,k) from (0,-2) =

According to the question:

⇒

Squaring both sides:

⇒

Again squaring both sides:

**⇒**

**⇒**

Replace (h,k) with (x,y)

Thus, the locus of a point such that sum of its distances from (0,2) and (0,-2) is 6:

**….proved**

Rate this question :

A rod of length l slides between the two perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.

RD Sharma - MathematicsFind the locus of a point which moves such that its distance from the origin is three times is the distance from the x-axis.

RD Sharma - MathematicsFind the locus of a point which is equidistant from (1, 3) and x-axis.

RD Sharma - MathematicsA point moves as so that the difference of its distances from (ae, 0) and (-ae, 0) is 2a, prove that the equation to its locus is , where b^{2} = a^{2}(e^{2} – 1).

If O is the origin and Q is a variable point on y^{2} = x, Find the locus of the mid-point of OQ.

A(5, 3), B(3, -2) are two fixed points, find the equation to the locus of a point P which moves so that the area of the triangle PAB is 9 units.

RD Sharma - MathematicsFind the locus of the mid-point of the portion of the x cos α + y sin α = p which is intercepted between the axes.

RD Sharma - MathematicsIf A (-1, 1) and B (2, 3) are two fixed points, find the locus of a point P so that the area d ΔPAB = 8 sq. units.

RD Sharma - MathematicsFind the locus of a point such that the line segments having end points (2, 0) and (-2, 0) subtend a right angle at that point.

RD Sharma - MathematicsFind the locus of a point such that the sum of its distances from (0, 2) and (0, -2) is 6.

RD Sharma - Mathematics