Find the Locus Equation: Distance Ratio of Points P, Q, and R

Solve for the equation of the locus of point R given the fixed points P(2,5) and Q(4,7) and the distance relationship 5|PR| = 3|QR|.

Answer

Let the coordinates of point

, point

, and point

.
We are given the condition

.
Squaring both sides of the equation, we get

, which simplifies to

The distance formula between two points

and

.
Therefore,

.
And

Substitute these into the squared equation:

Expand the squared terms:

Distribute the coefficients:

Combine like terms on each side:

Move all terms to one side to form the equation of the locus:

Simplify the terms:

Divide the entire equation by 4 to simplify:

This is the equation of the locus of

The final answer is

Related math solutions

Calculate Cylinder Height Given Diameter and Volume

Learn how to find the height of a cylinder using its diameter and volume with this step-by-step guide.

Finding the Missing Angle in an Isosceles Triangle

Calculate the value of x in an isosceles triangle with a vertex angle of 60 degrees by using the triangle angle sum property.

Area of a Road Around a Square Garden: S=at Proof

Learn how to prove that the area of a road surrounding a square garden is equal to the product of the road's width and the length of its centerline. This problem involves algebraic manipulation and geometric area calculations.

Dilation of a Polygon on a Coordinate Plane with a Scale Factor

Find the new coordinates of vertices E, F, G, and H after a dilation with a scale factor of 1/3 centered at the origin by multiplying each original coordinate by the scale factor.

Finding Angles with Parallel Lines and Transversal

Calculate the measures of angle 1 and angle 2 using the corresponding angle postulate and linear pair properties given a 63 degree angle.

Find the Locus Equation: Distance Ratio of Points P, Q, and R

Question

Answer

Related math solutions

웹 버전 영구 잠금 해제

Related math solutions